Probabilistic Reasoning Practice Questions

1. 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

2. 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

3. 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

4. If you flip a fair coin twice, what is the probability of getting at least one head?

1/4

1/2

3/4

1

5. 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

6. If the probability of rain on Monday is 0.3, on Tuesday is 0.4, and on Wednesday is 0.5, what is the probability that it will rain on at least one of these days? (Assume the events are independent)

0.79

0.82

0.85

0.88

7. 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

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

1/16

15/16

1/2

7/8

9. 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

10. If you roll two fair six-sided dice, what is the probability that the product of the two numbers is even?

1/4

1/3

1/2

3/4