Probabilistic Reasoning Practice Questions

1. If you draw two cards from a standard deck of 52 cards without replacement, what is the probability that both are aces?

1/221

1/169

1/121

1/91

2. In a standard deck of 52 cards, what is the probability of drawing a black card or a number card (2-10)?

17/26

35/52

19/26

39/52

3. In a class of 40 students, 25 play football and 20 play basketball. If 10 students play both sports, what is the probability that a randomly selected student plays at least one sport?

7/8

3/4

5/8

35/40

4. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are red?

1/6

2/9

1/3

5/18

5. 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

6. If the probability of rain on Saturday is 0.4 and the probability of rain on Sunday is 0.3, what is the probability that it will rain on both days? (Assume the events are independent)

0.12

0.7

0.58

0.1

7. If you randomly select a letter from the word "PROBABILITY", what is the probability of selecting a vowel?

2/11

3/11

4/11

5/11

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

1/6

5/36

1/4

7/36

9. In a group of 60 people, 35 like pizza and 40 like burgers. If 20 people like both pizza and burgers, how many people like neither?

5

10

15

20

10. If you roll a fair six-sided die three times, what is the probability of rolling at least one 6?

91/216

125/216

1/6

5/6