Probabilistic Reasoning Practice Questions

1. If the probability of rain on Saturday is 0.3 and the probability of rain on Sunday is 0.4, what is the probability that it will rain on at least one of these days? (Assume the events are independent)

0.58

0.7

0.12

0.42

2. A fair coin is tossed 10 times. What is the probability of getting exactly 5 heads?

63/256

63/512

252/1024

63/128

3. 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

4. If you roll a fair six-sided die, what is the probability of rolling a number that is either even or greater than 4?

1/3

1/2

2/3

5/6

5. 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

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

7/13

8/13

9/13

10/13

7. A fair six-sided die is rolled seven times. What is the probability of getting at least one 3?

1 - (5/6)^7

1 - (4/6)^7

1 - (3/6)^7

1 - (2/6)^7

8. A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is even?

1/4

1/3

1/2

2/3

9. 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

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