Probabilistic Reasoning Practice Questions

1. In a class of 30 students, 18 play basketball and 15 play soccer. If 10 students play both sports, how many students play neither sport?

5

7

8

9

2. In a group of 50 people, 30 speak English and 25 speak Spanish. If 10 people speak both languages, how many people speak at least one of the languages?

35

40

45

50

3. In a group of 100 people, 60 like coffee and 70 like tea. If 40 people like both coffee and tea, how many people like neither?

10

20

30

40

4. A bag contains 5 white balls and 7 black balls. Two balls are drawn at random without replacement. What is the probability that both balls are of the same color?

31/66

35/66

37/66

41/66

5. A fair coin is tossed 6 times. What is the probability of getting exactly 3 heads?

5/16

3/8

1/4

20/64

6. A bag contains 8 red marbles, 6 blue marbles, and 4 green marbles. Two marbles are drawn at random without replacement. What is the probability that both marbles are of the same color?

11/34

13/51

7/17

29/90

7. In a standard deck of 52 cards, what is the probability of drawing a heart or an even-numbered card?

25/52

13/26

27/52

7/13

8. 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

9. If the probability of an event A is 0.6 and the probability of event B is 0.7, what is the probability that at least one of the events does not occur? (Assume the events are independent)

0.58

0.7

0.82

0.88

10. In a standard deck of 52 cards, what is the probability of drawing a red card or a picture card (Jack, Queen, or King)?

7/13

8/13

9/13

10/13