Probability MCQ Questions & Answers

Probability MCQs : This section focuses on the "Probability". These Multiple Choice Questions (MCQs) should be practiced to improve the Probability skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

Question 1

Which of the following is not a correct statement about a probability.

A. A value near 0 means that the event is not likely to occur/happens

B. It can be reported as a decimal or a fraction

C. It must have a value between 0 and 1

D. It is the collection of several experiments

Question 2

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

A. 1/10

B. 2/5

C. 2/7

D. 5/7

Question 3

Two dice are rolled simultaneously. Find the probability of getting the sum of numbers on the on the two faces divisible by 3 or 4?

A. 3/7

B. 7/11

C. 5/9

D. 6/13

Question 4

The probability of occurance of two two events A and B are 1/4 and 1/2 respectively. The probability of their simultaneous occurrance is 7/50. Find the probability that neither A nor B occurs.

A. 25/99

B. 39/100

C. 61/100

D. 17/100

Question 5

Find the standard deviation of {11, 7, 10,13, 9}

A. 1

B. 2

C. 4

D. 5

Question 6

What is the probability that a number is divisible by 4?

A. 2

B. 1/2

C. 1/4

D. 1

Question 7

In a simultaneous throw of two dice, what is the probability of getting a total of 7 ?

A. 1/6

B. 1/4

C. 1/20

D. 3/4

Question 8

In a single throw with 2 dices, what is probability of neither getting an even number on one and nor a multiple of 3 on other?

A. 11/36

B. 25/36

C. 5/6

D. 1/6

Question 9

From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?

A. 19/5525

B. 16/5525

C. 17/5525

D. 7/5525

Question 10

If p:q are the odds in favour of an event,then the probability of that event is:

A. p/q

B. p/(p+q)

C. q/(p+q)

D. none

Question 11

One card is drawn from deck of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the ball drawn is red.

A. 1/3

B. 1/2

C. 1/4

D. 1/6

Question 12

What is the probability that a leap year selected at random, will contain 53 sundays?

A. 1/7

B. 1/3

C. 2/7

D. 4/7

Question 13

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

A. 1/15

B. 1/221

C. 25/57

D. 35/256

Question 14

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A. 10/11

B. 11/21

C. 2/7

D. 5/7

Question 15

A number is selected at random from the numbers 1 to 30. What is the probability that it is divisible by either 3 or 7 ?

A. 1/30

B. 2/30

C. 1/25

D. 1/2

Question 16

The probability that a card drawn at random from the pack of playing cards may be either a queen or an ace is:

A. 9/13

B. 11/13

C. 2/13

D. None of these

Question 17

The probabiltiy that throw of two dice yields a total of 5 or 6 is:

A. 2/14

B. 5/18

C. 3/4

D. 1/4

Question 18

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

A. 21/46

B. 1/5

C. 3/25

D. 1/50

Question 19

A number is selected from the numbers 1,2,3,4.......25.The probability for it to be divisible by 4 or 7 is:

A. 3/25

B. 9/25

C. 1/25

D. None of these

Question 20

Three unbiased coins are tossed. What is the probability of getting at most two heads?

A. 3/4

B. 7/8

C. 1/2

D. 1/4

Question 21

A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

A. 1/4

B. 1/2

C. 3/4

D. 7/12

Question 22

Binomial distribution is symmetrical when

A. p = q

B. p > q

C. p < q

D. np > npq

Question 23

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

A. 1/3

B. 3/5

C. 8/21

D. 7/21

Question 24

What is the probability that a leap year has 53 Saturdays and 52 Sundays ?

A. 1/7

B. 2/7

C. 1/2

D. 3/2

Question 25

The probability function is always

A. Negative

B. Non Negative

C. Positive

D. None of these

Question 26

A bag contains 3 red balls, 5 yellow balls and 7 pink balls. If one ball is drawn at random from the bag, what is the probability that it is either pink or red?

A. 2/3

B. 1/8

C. 3/8

D. 3/4

Question 27

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?

A. 2/3

B. 1/2

C. 7/8

D. 4/5

Question 28

Which of the following questions is a statistical question?

A. Where do the professional sports leagues play?

B. How many professional sports leagues are there?

C. How many hours do the student-athletes at your school spend each week training for a sports league?

D. How many hours of professional training took place over the weekend?

Question 29

If the occurrence of one event means that another cannot happen, then the events are

A. Bayesian

B. Empirical

C. Independent

D. Mutually Exclusive

Question 30

If a card is drawn at random from a pack of 52 cards,what is the chance of getting a spade or ace?

A. 0.25

B. 5/13

C. 0.2

D. 4/13

Question 31

In a box, there are four marbles of white color and five marbles of black color. Two marbles are chosen randomly. What is the probability that both are of the same color?

A. 2/9

B. 5/9

C. 4/9

D. 0

Question 32

What is the probability that a couple with four children have atleast one girl?

A. 0.0625

B. 0.9375

C. 0.5

D. 0.0257

Question 33

In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he. has offered English or Hindi ?

A. 1/2

B. 3/4

C. 4/5

D. 2/5

Question 34

A coin is tossed 5 times. What is the probability that head appears an odd number of times?

A. 1/2

B. 1/3

C. 2/3

D. 1

Question 35

The probabilities that drivers A, B and C will drive home safely after consuming liquor are 2 / 5, 3 / 7 and 3 / 4, respectively. What is the probability that they will drive home safely after consuming liquor ?

A. 3/70

B. 4/70

C. 9/70

D. 1/50

Question 36

Probability of occurrence of an event lies between

A. 0 and 1

B. -1 and 0

C. -1 and 1

D. exactly 1

Question 37

The probability that a number selected at random from the first 100 natural numbers is a composite number is ?

A. 3/2

B. 2/3

C. 1/2

D. 34/7

Question 38

There are 10 Letters and 10 correspondingly 10 different Address. If the letter are put into envelope randomly, then find the Probability that Exactly 9 letters will at the Correct Address ?

A. 1/10

B. 1/9

C. 1

D. 0

Question 39

There are 26 balls marked with alphabetical order A to Z. What is the probability of selecting vowels listed balls?

A. 1

B. 21/26

C. 5/26

D. 5

Question 40

Three unbiased coins are tossed. What is the probability of getting at most two heads?

A. 3/4

B. 1/4

C. 3/8

D. 7/8

Question 41

Out of 3 girls and 6 boys a group of three members is to be formed in such a way that at least one member is a girl. In how many different ways can it be done?

A. 64

B. 84

C. 56

D. 20

Question 42

From well shuffled standard pack of 52 playing cards,one card is drawn. What is the probability that it is either a red card or black card?

A. 1/2

B. 3/4

C. 1

D. 1/3

Question 43

Four dice are thrown simultaneously. Find the probability that two of them show the same face and remaining two show the different faces.

A. 4/9

B. 5/9

C. 11/18

D. 7/9

Question 44

A bag contains 5 red smileys, 6 yellow smileys and 3 green smileys. If two smileys are picked at random, what is the probability that both are red or both are green in colour?

A. 7

B. 1/7

C. 3/7

D. 0

Question 45

Two brother X and Y appeared for an exam. The probability of selection of X is 1/7 and that of B is 2/9. Find the probability that both of them are selected.

A. 1/63

B. 1/14

C. 2/63

D. 1/9

Question 46

Find the range of the data 2, 1, 2, 3, 5, 4, 7, 3, 5, 2, 4.

A. 5

B. 4

C. 3

D. 6

Question 47

Two cards are drawn at random from a well - shuffled pack of 52 cards. what is the probability that either both are red or both are queens?

A. 17/112

B. 55/221

C. 55/121

D. 33/221

Question 48

A number X is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that |X|<2

A. 3/7

B. 3/4

C. 4/5

D. 5/7

Question 49

A box contains 5 detective and 15 non-detective bulbs. Two bulbs are chosen at random. Find the probability that both the bulbs are non-defective.

A. 5/19

B. 3/20

C. 21/38

D. None of these

Question 50

Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.

A. 19/34

B. 5/4

C. 20/34

D. 25/34

Question 51

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:

A. 1/13

B. 2/13

C. 1/26

D. 1/52

Question 52

A three-digit number is formed with the digits 1, 2, 3, 4, 5 at random. What is probability that number formed is divisible by 5 ?

A. 1/4

B. 1/5

C. 1/2

D. 3/4

Question 53

A table tennis player, lost 12 games out of 18 games played. Calculate the games won in terms of decimal.

A. 0.667

B. 0.067

C. 0.5

D. 0.333

Question 54

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A. 1/2

B. 2/5

C. 8/15

D. 9/20

Question 55

The successive trials are with replacement in

A. Geometric distribution

B. Binomial distribution

C. Hypergeometric distribution

D. None of above

Question 56

In a purse there are 30 coins, twenty one-rupee and remaining 50-paise coins. Eleven coins are picked simultaneously at random and are placed in a box. If a coin is now picked from the box, find the probability of it being a rupee coin?

A. 4/7

B. 2/3

C. 1/2

D. 5/6

Question 57

A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A. 3/7

B. 4/7

C. 1/8

D. 3/4

Question 58

In a box, there are 9 blue, 6 white and some black stones. A stone is randomly selected and the probability that the stone is black is ¼. Find the total number of stones in the box?

A. 15

B. 18

C. 20

D. 24

Question 59

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

A. 6/7

B. 19/21

C. 7/31

D. 5/21

Question 60

A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.

A. 1/2

B. 7/15

C. 8/15

D. 1/9

Question 61

A brother and a sister appear for an interview against two vacant posts in an office. The probability of the brother’s selection is 1/5 and that of the sister’s selection is 1/3. What is the probability that only one of them is selected?

A. 1/5

B. 3/4

C. 2/5

D. 3/5

Question 62

Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?

A. 16/19

B. 1

C. 3/2

D. 17/20

Question 63

In special rule of addition of probability, the events are always

A. Bayesian

B. Empirical

C. Independent events

D. Mutually Exclusive events

Question 64

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

A. 1/15

B. 25/57

C. 35/256

D. 1/221

Question 65

A box contains 10 bulbs,of which just three are defective. If a random sample of five bulbs is drawn, find the probability that the sample contains exactly one defective bulb.

A. 5/12

B. 7/12

C. 3/14

D. 1/12

Question 66

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

A. 1/22

B. 3/22

C. 2/91

D. 2/77

Question 67

Three unbiased coins are tossed.What is the probability of getting at least 2 heads?

A. 1/4

B. 1/2

C. 3/4

D. 1/3

Question 68

If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?

A. 1

B. 1/2

C. 0

D. 3/5

Question 69

A card is drawn from a pack of 52 cards. The probability of getting a queen of the club or a king of the heart is?

A. 1/26

B. 1/13

C. 2/13

D. 1/52

Question 70

A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?

A. 136/345

B. 17/87

C. 316/435

D. 158/435

Question 71

If the standard deviation of a population is 4.5, what would be the population variance?

A. 20.25

B. 20

C. 9

D. 18

Question 72

A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident

A. 30/100

B. 35/100

C. 45/100

D. 50/100

Question 73

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A. 1/2

B. 3/5

C. 9/20

D. 8/15

Question 74

An unbiased die is rolled. Find the probability of getting a multiple of 3?

A. 1/6

B. 1/3

C. 5/6

D. None of these

Question 75

The mean of the data 2, 9, 9, 3, 6, 9, 4 is

A. 33/7

B. 6

C. 43/7

D. 7

Question 76

Find the range and mode of the data 17, 18, 28, 19, 16, 18, 17, 29, 18

A. 12 and 18

B. 13 and 18

C. 12 and 17

D. 11 and 17

Question 77

A bag contains 50 tickets numbered 1,2,3,4......50 of which five are drawn at random and arranged in ascending order of magnitude.Find the probability that third drawn ticket is equal to 30.

A. 551/15134

B. 1/2

C. 552/15379

D. 1/9

Question 78

If the standard deviation of a population is 7, what would be the population variance?

A. 14

B. 21

C. 49

D. 28

Question 79

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

A. 2/7

B. 5/7

C. 1/5

D. 1/2

Question 80

In a bag which contains 40 balls, there are 18 red balls and some green and blue balls. If two balls are picked up from the bag without replacement, then the probability of the first ball being red and second being green is 3/26. Find the number of blue balls in the bag.

A. 16

B. 12

C. 10

D. 14

Question 81

Tickets are numbered from 1 to 18 are mixed up together and then 9 tickets are drawn at random. Find the probability that the ticket has a number, which is a multiple of 2 or 3.

A. 1/3

B. 3/5

C. 2/3

D. 5/6

Question 82

Which of the following is not an example of a discrete probability distribution?

A. The number of bathrooms in a house

B. The sale or purchase price of a house

C. The number of bedrooms in a house

D. Whether or not a home has a swimming pool in it

Question 83

There are four hotels in a town. If 3 men check into the hotels in a day then what is the probability that each checks into a different hotel?

A. 1/2

B. 3/4

C. 4/7

D. 3/8

Question 84

8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :

A. 8/39

B. 15/39

C. 12/13

D. None of these

Question 85

The mean of a distribution is 18 and the standard deviation is 4.5. What is the value of the coefficient of variation?

A. 50%

B. 25%

C. 100%

D. 75%

Question 86

14 persons are seated around a circular table. Find the probability that 3 particular persons always seated together.

A. 11/379

B. 21/628

C. 24/625

D. 26/247

Question 87

You toss a coin AND roll a die. What is the probability of getting a tail and a 4 on the die?

A. 1/2

B. 1/12

C. 2/3

D. 3/4

Question 88

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

A. 23/42

B. 19/42

C. 7/32

D. 16/39

Question 89

Four dice are thrown simultaneously. Find the probability that all of them show the same face.

A. 1/216

B. 1/36

C. 2/216

D. 4/216

Question 90

A speaks truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, in narrating the same incident ?

A. 5%

B. 15%

C. 35%

D. 45%

Question 91

Which of the following is not the property of binomial distribution

A. N is fixed

B. Has two outcomes

C. Trials are independent

D. Probability of success varies from trial to trial

Question 92

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?

A. 6/19

B. 3/10

C. 7/10

D. 6/17

Question 93

A bag contains 8 red and 4 green balls. Find the probability that two balls are red and one ball is green when three balls are drawn at random.

A. 56/99

B. 112/495

C. 78/495

D. None of these

Question 94

The probability that a card drawn from a pack of 52 cards will be a diamond or a king, is

A. 5/12

B. 4/13

C. 5/13

D. 3/14

Question 95

Find the probability that it is either white or red ball when,one ball is drawn at random in a bag that contains 3 black,4 white and 5 red balls

A. 0.5

B. 0.75

C. 0.25

D. 0.8

Question 96

In a race, the odd favour of cars P,Q,R,S are 1:3, 1:4, 1:5 and 1:6 respectively. Find the probability that one of them wins the race.

A. 319/420

B. 27/111

C. 114/121

D. 231/420

Question 97

What is the probability of an impossible event?

A. 0

B. -1

C. 0.1

D. 1

Question 98

The distribution function F(X) is represented by

A. P(X)

B. P(X = x)

C. P(X > x)

D. P(X ≤ x)

Question 99

Three fair coins are tossed simultaneously. Find the probability of getting more heads than the number of tails

A. 2

B. 7/8

C. 5/8

D. 1/2

Question 100

If an unbiased dice is rolled once, the odds in favour of getting a point which is multiple of 3 is:

A. 1/2

B. 2/1

C. 1/3

D. 3/1

Question 101

Two dice are rolled simultaneously. Find the probability of getting a total of 9.

A. 1/3

B. 1/9

C. 8/9

D. 9/10

Question 102

Ajay and his wife Reshmi appear in an interview for two vaccancies in the same post. The Probability of Ajay's selection is 1/7 and that of his wife Reshmi's selection is 1/5. What is the probability that only one of them will be selected?

A. 5/7

B. 1/5

C. 2/7

D. 2/35

Question 103

The probability that z lies between 0 and 3.01

A. 0.4987

B. 0.5

C. 0.9987

D. 0.1217

Question 104

A speaks truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?

A. 35%

B. 5%

C. 45%

D. 22.50%

Question 105

If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?

A. 1/6

B. 1/2

C. 1/3

D. 1/4

Question 106

In which distribution successive trials are without replacement

A. Poisson distribution

B. Binomial distribution

C. Geometric distribution

D. Hypergeometric distribution

Question 107

The probabilities that A and B will tell the truth are 2 / 3 and 4 / 5 respectively . What is the probability that they agree with each other ?

A. 3/5

B. 1/3

C. 2/5

D. 3/4

Question 108

Two unbiased coin are tossed. What is the probability of getting atmost one head?

A. 1/2

B. 3/2

C. 1/6

D. 3/4

Question 109

Three dice are thrown together.Find the probability of getting a total of atleast 6.

A. 103/216

B. 103/108

C. 103/36

D. 36/103

Question 110

An unbiased die is tossed.Find the probability of getting a multiple of 3.

A. 1/3

B. 1/2

C. 3/4

D. 3/2

Question 111

Find the probability that one ball is white when two balls are drawn at random from a basket that contains 9 red, 7 white and 4 black balls.

A. 18/95

B. 18/190

C. 1/2

D. 91/190

Question 112

The variance of binomial distribution is always

A. Less than mean

B. Equal to mean

C. Greater than mean

D. Equal to standard deviation

Question 113

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

A. 21/42

B. 25/117

C. 1/50

D. 3/25

Question 114

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

A. 3/13

B. 1/13

C. 3/52

D. 9/52

Question 115

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A. 3/4

B. 3/8

C. 5/16

D. 2/7

Question 116

What is the probability of getting at least one six in a single throw of three unbiased dice?

A. 1/36

B. 91/256

C. 13/256

D. 43/256

Question 117

A letter is takenout at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

A. 35/96

B. 19/90

C. 19/96

D. None of these

Question 118

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

A. 1/3

B. 3/4

C. 7/19

D. 8/21

Question 119

The probability of success of three students X, Y and Z in the one examination are 1/5, 1/4 and 1/3 respectively. Find the probability of success of at least two.

A. 1/4

B. 1/2

C. 1/6

D. 1/3

Question 120

Find the median, mode and mean of 9, 5, 8, 9, 9, 7, 8, 9, 8.

A. 9, 9, 9

B. 9, 8, 9

C. 8, 9, 8

D. 8, 9, 9

Question 121

A discrete probability distribution may be represented by

A. A table

B. A graph

C. A mathematical Equation

D. All of these

Question 122

A room contains 3 brown, 5 black and 4 white chairs. Two chairs are picked and are put in the lawn. What is the probability that none of the chairs picked is white ?

A. 14/33

B. 14/55

C. 12/55

D. 13/33

Question 123

Find the probability of selecting exactly 2 children when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.

A. 9/29

B. 10/21

C. 12/21

D. 14/19

Question 124

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A. 1/2

B. 3/4

C. 3/8

D. 5/16

Question 125

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 12?

A. 35/36

B. 17/36

C. 15/36

D. 1/36

Question 126

A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A. 1/6

B. 1/3

C. 1/2

D. 1/4

Question 127

Two dice are tossed. The probability that the total score is a prime number is:

A. 1/6

B. 5/12

C. 1/2

D. 7/9

Question 128

If x is chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even?

A. 1/2

B. 2/3

C. 3/4

D. 4/3

Question 129

In a simultaneous throw of pair of dice. Find the probability of getting the total more than 7.

A. 1/2

B. 5/12

C. 7/15

D. 3/12

Question 130

The probability of success changes from trial to trial in

A. Sampling distribution

B. Binomial distribution

C. Hypergeometric distribution

D. Geometric distribution

Question 131

Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval ?

A. [1, 32]

B. (0, 1)

C. [1, 1/2]

D. (1, 1/2]

Question 132

An urn contains 4 white 6 black and 8 red balls . If 3 balls are drawn one by one without replacement, find the probability of getting all white balls.

A. 5/204

B. 1/204

C. 13/204

D. None of these

Question 133

A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:

A. 123/897

B. 23/67

C. 7/44

D. 12/45

Question 134

Two dice are tossed. The probability that the total score is a prime number is :

A. 1/6

B. 1/2

C. 5/12

D. 3/4

Question 135

What is the probability of getting a sum 9 from two throws of a dice ?

A. 1/6

B. 1/2

C. 1/9

D. 3/4

Question 136

One lady has 2 children, one of her child is boy, what is the probability of having both are boys ?

A. 1/3

B. 1/2

C. 2/3

D. 2/5

Question 137

A fair coin is tossed 11 times. What is the probability that only the first two tosses will yield heads ?

A. (1/2)^11

B. (9)(1/2)

C. (11C2)(1/2)^9

D. (1/2)

Question 138

For a random variable X, E(X) is

A. Harmonic Mean (HM)

B. Geometric Mean (GM)

C. Arithmetic Mean (AM)

D. None of these

Question 139

What is the probabiltiy of getting a mutliple of 2 or 5 when an unbiased cubic die is thrown?

A. 1/3

B. 1/2

C. 2/3

D. 1/6

Question 140

One card is drawn from a pack of 52 cards , each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is neither a spade nor a king.

A. 0

B. 9/13

C. 1/2

D. 4/13

Question 141

The letters of the word CASTIGATION is arranged in different ways randomly. What is the chance that vowels occupy the even places ?

A. 0.04

B. 0.043

C. 0.047

D. 0.05

Question 142

Binomial distribution has parameters

A. 1

B. 2

C. 3

D. 4

Question 143

In which approach to probability the outcomes are equally likely to occur?

A. Classical Probability

B. Subjective Probability

C. Relative Frequency

D. Independent

Question 144

Each trial in Binomial distribution has

A. One Outcome

B. Two Outcome

C. Three Outcome

D. Four Outcome

Question 145

Three unbiased coins are tossed. What is the probability of getting at most two heads ?

A. 4/3

B. 2/3

C. 3/2

D. 3/4

Question 146

A five digit number is formed with the digits 0,1,2,3 and 4 without repetition. Find the chance that the number is divisible by 5.

A. 3/5

B. 1/5

C. 2/5

D. 4/5

Question 147

A bag contains 3 black, 4 white and 5 red balls. One ball is drawn at random. Find the probability that it is either black or red ball:

A. 2/3

B. 1/4

C. 5/12

D. 1/2

Question 148

fifteen persons are sitting around a circular table facing the centre. What is the probability that three particular persons sit together ?

A. 3/91

B. 2/73

C. 1/91

D. 3/73

Question 149

In a throw of a coin, find the probability of getting a head.

A. 1

B. 1/2

C. 1/4

D. 0.1

Question 150

Four persons are to be choosen from a group of 3 men, 2 women and 4 children. Find the probability of selecting 1 man,1 woman and 2 children.

A. 2/7

B. 3/7

C. 4/7

D. 3/7

Question 151

The mean, median and mode for binomial distribution will be equal when

A. p = 0.5

B. p < 0.5

C. p > 0.5

D. p = 1

Question 152

A group of five persons is formed from five boys and four girls. Find the probability that there are at least two girls in the group?

A. 110/129

B. 5/6

C. 121/126

D. 3/7

Question 153

If a box contains 10 bulbs,of which just three are defective. If a random sample of five bulbs is drawn, find the probability that the sample contains no defective bulbs.

A. 5/12

B. 7/12

C. 3/14

D. 1/12

Question 154

Two dice are tossed. The probability that the total score is a prime number is:

A. 5/12

B. 1/6

C. 1/2

D. 7/9

Question 155

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

A. 1/13

B. 3/13

C. 1/4

D. 9/52

Question 156

Two letters are randomly chosen from the word TIME. Find the probability that the letters are T and M?

A. 1/4

B. 1/6

C. 1/8

D. 4

Question 157

X attempts 94 questions and gets 141 marks. If for every correct answer 4 marks is given, and for every wrong answer 1 mark is deducted, then the number of questions wrongly answered by X is __.

A. 45

B. 47

C. 57

D. 40

Question 158

A man and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is (1/7) and the probability of wife's selection is (1/5). What is the probability that only one of them is selected ?

A. 2/7

B. 1/7

C. 3/4

D. 4/5

Question 159

An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4?

A. 1/12

B. 1/9

C. 3/4

D. 1/2

Question 160

The mean of a distribution is 15 and the standard deviation is 5. What is the value of the coefficient variation?

A. 16.66%

B. 66.66%

C. 33.33%

D. 100%

Question 161

Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?

A. 52/221

B. 55/190

C. 55/221

D. 19/221

Question 162

The collection of one or more outcomes from an experiment is called

A. Event

B. Z-Value

C. Probability

D. Random Variable

Question 163

The Manager of a company accepts only one employees leave request for a particular day. If five employees namely Roshan, Mahesh, Sripad, Laxmipriya and Shreyan applied for the leave on the occasion of Diwali. What is the probability that Laxmi priya’s leave request will be approved ?

A. 1

B. 1/5

C. 5

D. 4/5

Question 164

In a simultaneous throw of two dice, what is the probability of getting a doublet ?

A. 1/6

B. 1/3

C. 4/7

D. 4/5

Question 165

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn find the probability the card drawn is red.

A. 2/3

B. 1/2

C. 1/52

D. 13/51

Question 166

What is the probability of getting a sum 9 from two throws of a dice?

A. 1/6

B. 1/8

C. 1/9

D. 1/12

Question 167

In a Poisson probability distribution

A. It always contains a contingency table

B. The number of trials is always less than 5

C. The probability of success is always greater than 5

D. The mean and variance of the distribution are same (equal)

Question 168

A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?

A. 1/6

B. 2/3

C. 14/33

D. 5/6

Question 169

The mean of 20 observations is 19. One more observation is included and the new mean becomes 20. The 21st observation is

A. 20

B. 30

C. 40

D. 42

Question 170

If the difference between the mode and median is 2, then the difference between the median and mean is:

A. 2

B. 1

C. 3

D. 4

Question 171

What is the probability of getting 53 Mondays in a leap year?

A. 1/7

B. 3/7

C. 2/7

D. 1

Question 172

In a single throw of two dice , find the probability that neither a doublet nor a total of 8 will appear.

A. 7/15

B. 5/18

C. 13/18

D. 3/16

Question 173

The standard deviation of the set {10, 11, 12, 9, 8} is

A. 1

B. √2

C. 2

D. 2√2

Question 174

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A. 10/21

B. 11/21

C. 1/2

D. 2/7

Question 175

Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King

A. 1/52

B. 1/26

C. 1/13

D. 1/2

Question 176

A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely. Find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail

A. 1/3

B. 2/3

C. 2/5

D. 4/15

Question 177

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

A. 2/9

B. 1/9

C. 8/9

D. 7/9

Question 178

A six-sided die with faces numbered 1 through 6 is rolled three times. What is the probability that the face with the number 6 on it will not face upward on all the three rolls?

A. 215/216

B. 1/216

C. 215/256

D. 1/52

Question 179

The mean of a distribution is 20 and the standard deviation is 4. What is the value of the coefficient variation?

A. 10%

B. 20%

C. 40%

D. 60%

Question 180

A card is drawn from a pack of 52 cards. The card is drawn at random. What is the probability that it is neither a spade nor a Jack?

A. 9/13

B. 4/13

C. 10/13

D. 8/13

Question 181

In hypergeometric distribution, the trials are

A. Dependent

B. Independent

C. Collectively Exhaustive

D. None of these

Question 182

The the special rule of multiplication of probability, the events must be

A. Empirical

B. Bayesian

C. Independent

D. Independent

Question 183

I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?

A. 1/999

B. 1/1001

C. 1/1000

D. 4/1000

Question 184

A listing of the possible outcomes of an experiment and their corresponding probability is called

A. Bayesian table

B. Random Variable

C. Contingency table

D. Probability distribution

Question 185

Which of the following is not a condition of the binomial distribution?

A. trials must be independent

B. must have at least 3 trials

C. only 2 possible outcomes

D. have constant probability of success

Question 186

Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6.

A. 7/18

B. 14/35

C. 8/18

D. 7/35

Question 187

Find the probability of selecting 2 woman when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.

A. 1/5

B. 1/7

C. 1/6

D. 1/9

Question 188

If the standard deviation of a population is 6.5, what would be the population variance?

A. 40.25

B. 42.25

C. 18.25

D. 13

Question 189

One card is drawn from a pack of 52 cards,each of the 52 cards being equally likely to be drawn.Find the probability that the ball drawn is an ace :

A. 1/13

B. 1/12

C. 1/14

D. 1/15

Question 190

The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on at least one ticket is -

A. 0.4869

B. 0.5904

C. 0.6234

D. 0.5834

Question 191

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

A. 2/91

B. 1/22

C. 3/22

D. 2/77

Question 192

Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion?

A. 3 to 2

B. 5 to 2

C. 6 to 1

D. 33 to 7

Question 193

What is the probability of getting a sum 9 from two throws of a dice?

A. 1/2

B. 3/4

C. 1/9

D. 2/9

Question 194

The first 8 alphabets are written down at random. what is the probability that the letters b,c,d,e always come together ?

A. 1/7

B. 8!

C. 7!

D. 1/14

Question 195

In a charity show tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random (blindly) will have a number with a hundredth digit of 2?

A. 0.25

B. 0.5

C. 0.75

D. 0.4

Question 196

The odds favouring the event of a person hitting a target are 3 to 5. The odds against the event of another person hitting the target are 3 to 2. If each of them fire once at the target, find the probability that both of them hit the target.

A. 1/20

B. 4/20

C. 1/20

D. 3/20

Question 197

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize ?

A. 1/7

B. 2/7

C. 3/7

D. 2/5

Question 198

Successive trials in binomial distribution are

A. Dependent

B. Independent

C. Equally Likely

D. Mutually exclusive

Question 199

The variance of a set of data is 121. Then the standard deviation of the data is

A. +-11

B. 11

C. 21

D. 60.5

Question 200

Hypergeometric distribution has parameters

A. 1

B. 2

C. 3

D. 4

Question 201

Three unbiased coins are tossed. What is the probability of getting at least 2 tails?

A. 0.75

B. 0.5

C. 0.25

D. 0.2

Question 202

A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A. 3/4

B. 4/7

C. 1/8

D. 3/7

Question 203

A speaks truth in 75% cases and B in 80% of cases. In what percentage of cases they contradict each other in narrating the same incident?

A. 15%

B. 25%

C. 35%

D. 45%

Question 204

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

A. 3/20

B. 29/34

C. 47/100

D. 13/102

Question 205

What is the probability that it is either a heart card or diamond card, when a card is drawn from a well shuffled standard pack of 52 playing cards?

A. 1

B. 1/2

C. 3/4

D. 1/3

Question 206

A fair six-sided die is rolled twice. What is the probability of getting 4 on the first roll and not getting 6 on the second roll ?

A. 1/36

B. 5/36

C. 1/12

D. 1/9

Question 207

A speaks truth in 60% cases B speaks truth in 70% cases. The probability that they will way say the same thing while describing a single event, is-

A. 0.54

B. 0.56

C. 0.68

D. 0.94

Question 208

The probabilities that a student will receive an A, B, C or D grade are 0.4, 0.3 , 0.2 and 0.1 respectively. Find the probability that a student will receive Atleast B grade.

A. 0.21

B. 0.3

C. 0.7

D. None of these

Question 209

If the standard deviation of a population is 10, what would be the population variance?

A. 100

B. 30

C. 5

D. 20

Question 210

A person starting with 64 rupees and making 6 bets, wins three times and loses three times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is:

A. A gain of Rs. 27

B. A loss of Rs. 37

C. A loss of Rs. 27

D. A gain of Rs. 37

Question 211

Out of sixty students, there are 14 who are taking Economics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the Calculus class ?

A. 8/15

B. 7/15

C. 1/15

D. 4/15

Question 212

The probability that a bowler bowled a ball from a point will hit by the batsman is ¼. Three such balls are bowled simultaneously towards the batsman from that very point. What is the probability that the batsman will hit the ball ?

A. 37/64

B. 27/56

C. 11/13

D. 9/8

Question 213

The mean of distribution is 11 and the standard deviation is 5. What is the value of the coefficient variation?

A. 45.45%

B. 35.35%

C. 25.25%

D. 55.55%