Probabilistic Reasoning Practice Questions

1. 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

2. 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

3. If the probability of event A is 0.7 and the probability of event B is 0.6, what is the probability of both events occurring if they are independent?

0.13

0.42

0.3

0.58

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

5/16

3/8

1/4

20/64

5. A bag contains 6 red marbles and 8 blue marbles. If you draw two marbles without replacement, what is the probability that they are of different colors?

12/35

24/35

1/2

2/3

6. If the probability of an event A is 0.3 and the probability of event B is 0.5, what is the probability of both events occurring if they are independent?

0.15

0.2

0.35

0.8

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

4/13

13/52

16/52

17/52

8. A fair coin is tossed 5 times. What is the probability of getting at least 4 heads?

5/32

3/16

11/32

21/32

9. In a group of 100 people, 40% are male. If a person is selected at random, what is the probability that the person is female?

0.4

0.5

0.6

0.7

10. A box contains 3 red balls, 4 blue balls, and 5 green balls. If you draw three balls without replacement, what is the probability that you draw one of each color?

1/4

1/3

5/12

1/2