Probabilistic Reasoning Practice Questions

1. In a deck of 52 cards, what is the probability of drawing a face card (Jack, Queen, or King) or an Ace?

4/13

1/4

7/13

1/3

2. A bag contains 12 white balls, 8 black balls, and 6 red balls. Three balls are drawn at random without replacement. What is the probability that all three balls are of different colors?

11/65

13/65

17/65

19/65

3. A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?

1/6

1/4

5/36

1/12

4. A fair coin is tossed 4 times. What is the probability of getting at least one head?

15/16

7/8

3/4

1/2

5. A bag contains 3 red marbles, 4 blue marbles, and 5 green marbles. If you draw two marbles without replacement, what is the probability that they are of different colors?

37/66

29/66

1/2

2/3

6. In a group of 100 people, 60 like coffee, 70 like tea, and 40 like both. What is the probability that a randomly selected person likes either coffee or tea?

0.6

0.7

0.8

0.9

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 six-sided die is rolled four times. What is the probability of getting at least one 5?

625/1296

671/1296

5/6

11/16

9. In a group of 80 people, 45 speak English and 55 speak French. If 30 people speak both languages, how many people speak neither language?

5

10

15

20

10. If the probability of an event A is 0.3 and the probability of event B is 0.4, what is the probability that exactly one of the events occurs? (Assume the events are independent)

0.42

0.46

0.58

0.7