Probabilistic Reasoning Practice Questions

1. If you draw a card from a standard deck and then draw a second card without replacing the first, what is the probability that both cards are spades?

1/4

1/13

1/16

1/17

2. If the probability of event A is 0.4 and the probability of event B is 0.5, what is the probability of either A or B occurring if they are not mutually exclusive and P(A and B) = 0.1?

0.7

0.8

0.9

1.0

3. If the probability of an event A is 0.4 and the probability of event B is 0.5, what is the minimum possible probability of both events occurring?

0

0.1

0.2

0.3

4. In a standard deck of 52 cards, what is the probability of drawing a face card (Jack, Queen, or King) or a club?

5/13

6/13

7/13

8/13

5. If the probability of an event A is 0.3 and the probability of event B is 0.4, what is the probability that both events occur? (Assume the events are independent)

0.1

0.12

0.7

0.58

6. In a group of 80 people, 45 speak English, 35 speak French, and 15 speak both languages. What is the probability that a randomly selected person speaks exactly one of these languages?

1/2

5/8

3/4

7/8

7. In a standard deck of 52 cards, what is the probability of drawing a king or a spade?

4/13

13/52

16/52

17/52

8. If the probability of an event A is 0.6 and the probability of event B is 0.5, what is the maximum possible probability of both events occurring?

0.3

0.5

0.6

1.1

9. A fair coin is tossed 25 times. What is the probability of getting exactly 12 heads?

0.1715

0.1755

0.1795

0.1835

10. In a standard deck of 52 cards, what is the probability of drawing a red card or an ace?

13/26

27/52

14/26

29/52