Question

1) Suppose you have the following information. 12% of all drivers do not have a valid driver’s license, 6% of all drivers have no insurance, and 4% have neither (i.e., do not have driver’s license and do not have insurance). The probability that a randomly selected driver either fails to have a valid license or fails to have insurance is about

(a) 0.18

(b) 0.2

(c) 0.22

(d) 0.072

(e) 0.14

3) Given that events A and B are mutually exclusive, i.e., A?B = ? and P(A?B) =0, and that P(A)=0.7 and P(B)=0.2, find P(A or B).

(a) 0.14

(b) 0.9

(c) 0.5

(d) 0.76

(e)1.04

4). A coin is flipped and a six-diced die is rolled. What is the probability that the coin lands heads and the die shows four or more? (Hint: define A to be the event ‘coin lands heads’ and B to be the event ‘die shows four or more’. A and B are independent events, since the coin flip has nothing to do with the coin toss. The probability that both events will occur is the product of the two individual probabilities.)

(a) 0.5

(b) 1

(c) 0.25

(d) 0.75

(e) none of the above

5). A single fair die is rolled. Let events A={2,4}, and B={1,2,5}. Event A is independent with event B. True or False?

6). A single fair die is rolled. What if event A stays the same, i.e., A={2,4} but B={2,4,5}. Event A is independent with event B. True or False?

7). A card is selected at random from a well-shuffled ordinary deck consisting of 13 spades, 13 clubs, 13 hearts, and 13 diamonds. 4 Jacks, 4 Queens, and 4 Kings are ‘face’ cards. The probability that the card is a heart or is a face card is about

(a) 0.23

(b) 0.42

(c) 0.19

(d) 0.48

(e) 0.25

Answer 1

1) Probability = 0.12 + 0.06 - 0.04 = 0.14

Option - e is correct.

3) P(A or B) = P(A) + P(B)

                    = 0.7 + 0.2 = 0.9

Option - B is correct.

4) Probability = 3 * (0.5 * (1/6)) = 0.25

Option - C is correct.

5) P(A) = 2/6

    P(B) = 3/6

    P(A and B) = 1/6

P(A) * P(B) = 2/6 * 3/6 = 1/6

Since P(A and B) = P(A) * P(B), so events A and B are independent.

So it is True.

6) P(A) = 2/6

    P(B) = 3/6

    P(A and B) = 2/6

P(A) * P(B) = 2/6 * 3/6 = 1/6

Since P(A and B) P(A) * P(B), so events A and B are not independent.

So it is false.

7) P(heart or face card) = 13/52 + 12/52 - 3/52

                                     = 22/52 = 0.42

Option - b is correct.