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QUESTION: 1

(Direction 1 - 22) Write down the correct answers. Each question carries 5 marks.

**Q. If two unbiased dice are rolled, what is the probability of getting points neither 6 nor 9?**

Solution:

QUESTION: 2

What is the probability that 4 children selected at random would have different birthdays?

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QUESTION: 3

A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectively

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QUESTION: 4

There are three boxes with the following composition:

Box I: 5 Red + 7 White + 6 Blue balls

Box II: 4 Red + 8 White + 6 Blue balls

Box III: 3 Red + 4 White + 2 Blue balls

If one ball is drawn at random, then what is the probability that they would be of same colour?

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QUESTION: 5

A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?

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QUESTION: 6

A bag contains 8 red and 5 white balls. Two successive draws of 3 balls are made without replacement. The probability that the first draw will produce 3 white balls and the second 3 red balls is

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QUESTION: 7

There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is

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QUESTION: 8

A problem in probability was given to three CA students A, B and C whose chances of solving it are 1/3, 1/5 and 1/2 respectively. What is the probability that the problem would be solved?

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QUESTION: 9

There are three persons aged 60, 65 and 70 years old. The survivals probabilities for these three persons for another 5 years are 0.7, 0.4 and 0.2 respectively. What is the probability that at least two of them would survive another five years?

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QUESTION: 10

Tom speaks truth in 30 percent cases and Dick speaks truth in 25 percent cases. What is the probability that they would contradict each other?

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QUESTION: 11

There are two urns. The first urn contains 3 red and 5 white balls whereas the second urn contains 4 red and 6 white balls. A ball is taken at random from the first urn and is transferred to the second urn. Now another ball is selected at random from the second arm. The probability that the second ball would be red is

Solution:

QUESTION: 12

For a group of students, 30 %, 40% and 50% failed in Physics , Chemistry and at least one of the two subjects respectively. If an examinee is selected at random, what is the probability that he passed in Physics if it is known that he failed in Chemistry?

Solution:

Let the total number of students = 100

Number of students failed in physics = 30% of 100 =30

Number of students failed in chemistry = 40% of 100 =40

Number of students failed at least one of the two subjects = 50% of 100 =50

We need to calculate

QUESTION: 13

A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective?

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QUESTION: 14

8 identical balls are placed at random in three bags. What is the probability that the first bag will contain 3 balls?

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QUESTION: 15

X and Y stand in a line with 6 other people. What is the probability that there are 3 persons between them?

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QUESTION: 16

Given that P (A) = 1/2, P (B) = 1/3, P (A ∩ B) = 1/4, what is P (A’/B’)

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QUESTION: 17

Four digits 1, 2, 4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4?

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QUESTION: 18

The probability distribution of a random variable x is given below:

**Q. What is the standard deviation of x? **

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QUESTION: 19

A packet of 10 electronic components is known to include 3 defectives. If 4 components are selected from the packet at random, what is the expected value of the number of defective?

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QUESTION: 20

The probability that there is at least one error in an account statement prepared by 3 persons A, B and C are 0.2, 0.3 and 0.1 respectively. If A, B and C prepare 60, 70 and 90 such statements, then the expected number of correct statements

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QUESTION: 21

A bag contains 6 white and 4 red balls. If a person draws 2 balls and receives Rs.10 and Rs.20 for a white and red balls respectively, then his expected amount is

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QUESTION: 22

The probability distribution of a random variable is as follows:

**Q. The variance of x is **

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QUESTION: 23

All possible outcomes of a random experiment forms the

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QUESTION: 24

If one of outcomes cannot be expected to occur in preference to the other in an experiment the events are

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QUESTION: 25

If two events cannot occur simultaneously in the same trial then they are

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QUESTION: 26

When the no. of cases favourable to the event A=0 then P(A) is equal to

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QUESTION: 27

A card is drawn from a well-shuffled pack of playing cards. The probability that it is a spade is

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QUESTION: 28

A card is drawn from a well-shuffled pack of playing cards. The probability that it is a king is

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QUESTION: 29

A card is drawn from a well-shuffled pack of playing cards. The probability that it is the ace of clubs is

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QUESTION: 30

In a single throw with two dice the probability of getting a sum of five on the two dice is

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QUESTION: 31

In a single throw with two dice, the probability of getting a sum of six on the two dice is

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QUESTION: 32

The probability that exactly one head appears in a single throw of two fair coins is

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QUESTION: 33

The probability that at least one head appears in a single throw of three fair coins is

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QUESTION: 34

The definition of probability fails when the no of possible outcomes of the experiment is infinite

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QUESTION: 35

The following table gives distribution of wages of 100 workers –

**Q. The probability that his wages are under Rs.140 is**

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QUESTION: 36

An individual is selected at random from the above group. The probability that his wages are under Rs.160 is

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QUESTION: 37

For the above table the probability that his wages are above Rs.200 is

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QUESTION: 38

For the above table the probability that his wages between Rs.160 and 220 is

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QUESTION: 39

The table below shows the history of 1000 men :

**Q. The probability that a man will survived to age 90 is **

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QUESTION: 40

The terms “chance” and probability are synonymous

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