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Question 1

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A die is rolled. What is the probability of rolling an even number?

Select the correct option.

Select one:

1. 1/6
2. 2/3
3. 1/2
4. 1/4

Question 2

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Alice rolls two dice. What is the probability of rolling two 6s?

Select the correct option.

Select one:

1. 1/36
2. 1/6
3. 1/18
4. 1/12

Question 3

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A prisoners’ dilemma is a game with all of the following characteristics except one. Choose the characteristic that is not applicable to a prisoners’ dilemma game

Select the correct option.

Select one:

1. Both players would get higher payoffs if none of them chose the dominant strategy
2. Both players have a dominant strategy
3. Players cooperate and select their strategies
4. The payoff from one player’s strategy depends on the choice by the other player

Question 4

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Bob randomly picks a number from 1 to 6 (both inclusive). What is the probability that he picks a number more than 3?

Select the correct option.

Select one:

1. 0.4
2. 0.2
3. 0.3
4. 0.5

Question 5

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When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?

Select the correct option.

Select one:

1. 5/6
2. 1/12
3. 1/6
4. 11/12

Question 6

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A pair of dice is rolled till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is :

Select the correct option.

Select one:

1. 0.5
2. 0.45
3. 0.4
4. 0.6

Question 7

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A bag contains 3 white and 5 black balls. Alice draws two balls one after another from the bag, without replacement. What is the probability that the first ball is white and the second black?

Select the correct option.

Select one:

1. 12/36
2. 15/64
3. 2/28
4. 15/56

Question 8

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For the game shown below, identify the mixed strategy Nash equilibrium where ‘p’ is the probability that Bob chooses A and ‘q’ is the probability that Mary chooses C

Select the correct option.

Select one:

1. (p=1/3, q=1/3)
2. (p=1/3, q=2/3)
3. (p=1/2, q=1/2)
4. (p=2/3, q=2/3)

Question 9

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A box contains 4 red pencils and 5 blue pencils. 4 pencils are taken out one after the other without replacement. What is the probability that the pencils drawn are red, blue, blue and red in that order (approximated to two decimal places)?

Select the correct option.

Select one:

1. 0.09
2. 0.06
3. 0.07
4. 0.08

Question 10

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A group of children has 2 boys and 2 girls. 2 children are selected from the group. What is the probability that a boy and a girl get selected?

Select the correct option.

Select one:

1. a. 1 /4
2. 1/6
3. 2/3
4. 1/2

Question 11

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If the probability that an event occurs is ‘p’ and the probability that the event does not occur is ‘q’, which of the following is necessarily true?

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Select one:

1. P^2+q^2=1
2. p(1-q)+q(1-p)+2(1-p)(1-q)=1
3. p-q>0
4. (p+q)(p-q)=1

Question 12

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A coin is tossed once. What is the probability of getting heads or tails?

Select the correct option.

Select one:

1. 0.5
2. 0
3. 1
4. 0.25

Question 13

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If the probability of an event to occur is 0.4. What is the probability that the event will not occur?

Select the correct option.

Select one:

1. 0.6
2. 0.4
3. 0.7
4. 0.5

Question 14

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

Select the correct option.

Select one:

1. 1/2
2. 1/4
3. 3/4
4. 11/12

Question 15

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John randomly picks a number from 1 to 5 (both inclusive) and a letter from A to E (both inclusive). What is the probability that he picks 2 and E?

Select the correct option.

Select one:

1. 1/5
2. 1/25
3. 1/30
4. 1/4

Question 16

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A game matrix is shown below:

Choose the correct statement among the following:

Select the correct option.

Select one:

1. Run is the dominant strategy for Bob
2. Both players have a dominant strategy
3. If Bob chooses Run, Alice’s best response is Run
4. (Run, Run) is the Nash equilibrium

Question 17

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A fair dice is tossed 6 times. Find the probability of getting a third six on the sixth throw.

Select the correct option.

Select one:

1. ⁵C₃x 5² / 6⁶
2. ⁵C₂x 5² / 6⁶
3. ⁵C₂x 5⁴ / 6⁶
4. ⁵C₂x 5³ / 6⁶

Question 18

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Alice rolls two dice. What is the probability of obtaining at least one 6?

Select the correct option.

Select one:

1. 1/24
2. 1/6
3. 10/36
4. 11/36

Question 19

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For the game shown below, identify the mixed strategy Nash equilibrium where ‘p’ is the probability that Bob chooses A and ‘q’ is the probability that Mary chooses C

Select the correct option.

Select one:

1. (p=2/3, q=2/3)
2. (p=1/3, q=2/3)
3. (p=1/2, q=1/2)
4. (p=1/3, q=1/3)

Question 20

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A bag contains 3 white and 5 black balls. Bob draws two balls one after another from the bag, without replacement. What is the probability that any one ball is white and the other is black?

Select the correct option.

Select one:

1. 25/56
2. 45/56
3. 15/28
4. 15/56

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