Q: Which of the following is the correct formula for the probability of event $$A$$ given event $$B$$ has occurred?

$$P(A|B) = \frac{P(A \text{ AND } B)}{P(B)}$$

Q: If two events $$A$$ and $$B$$ are independent, which of the following is true?

$$P(A \text{ AND } B) = P(A) \times P(B)$$

Q: A random experiment consists of rolling a die. Let $$A be $$the event 'roll an even number' and $$B be $$the event 'roll a number greater than 3'. Are $$A$$ and $$B$$ independent?

Yes, because $$P(A \text{ AND } B) = P(A) \times P(B)$$

Question 1

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 2

Suppose you flip a fair coin three times. What is the probability of getting exactly two heads?

Accepted Answer

$$\frac{3}{8}$$

Question 3

In a group of 665 people, 143 have a college education. If one person is selected at random, what is the probability that the person has a college education?

Accepted Answer

$$\frac{143}{665}$$

Question 4

If two events $$A$$ and $$B$$ are mutually exclusive, which of the following is true?

Accepted Answer

$$P(A 	ext{ AND } B) = 0$$

Question 5

A table shows that out of 126 students, 39 are Democrats who support legalization of cannabis, and 43 students in total support legalization. What is the probability that a randomly selected student supports legalization given that they are a Democrat?

Accepted Answer

$$\frac{39}{64}$$

Question 6

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of trials increases, the empirical probability of an event approaches its theoretical probability.

Question 7

Suppose you roll two fair dice and add the outcomes. What is the probability that the sum is 6?

Accepted Answer

$$\frac{5}{36}$$

Question 8

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ AND } B) = 0.2$$, what is $$P(A 	ext{ OR } B)$$?

Accepted Answer

$$0.9$$

Question 9

A person is selected at random from a group. The probability that the person is married is $$\frac{408}{665}$$, and the probability that the person has a college education is $$\frac{143}{665}. $$The probability that the person is married AND has a college education is $$\frac{98}{665}. $$What is the probability that the person is married OR has a college education?

Accepted Answer

$$\frac{551}{665}$$

Question 10

Which of the following is the correct formula for the probability of event $$A$$ given event $$B$$ has occurred?

Accepted Answer

$$P(A|B) = \frac{P(A 	ext{ AND } B)}{P(B)}$$

Question 11

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

$$P(A 	ext{ AND } B) = P(A) 	imes P(B)$$

Question 12

A die is rolled. Let $$A be $$the event that the die shows an even number, and $$B be $$the event that the die shows a number greater than 4. What is $$P(A 	ext{ OR } B)$$?

Accepted Answer

$$\frac{5}{6}$$

Question 13

Which of the following statements about mutually exclusive events is correct?

Accepted Answer

If two events are mutually exclusive, they cannot both occur at the same time.

Question 14

A survey of 126 students found that 25 are Republicans who support legalization of cannabis, and 40 are Republicans in total. What is the probability that a randomly selected Republican supports legalization?

Accepted Answer

$$\frac{25}{40}$$

Question 15

Suppose you roll a fair six-sided die. What is the probability that the die shows an even number OR the number 5?

Accepted Answer

$$\frac{4}{6}$$

Question 16

Which of the following is NOT a requirement for a set of numbers to be a probability distribution?

Accepted Answer

Each probability must be greater than 1.

Question 17

If $$P(A) = 0.3$$ and $$P(B|A) = 0.5$$, what is $$P(A 	ext{ AND } B)$$?

Accepted Answer

$$0.15$$

Question 18

A random experiment consists of rolling a die. Let $$A be $$the event 'roll an even number' and $$B be $$the event 'roll a number greater than 3'. Are $$A$$ and $$B$$ independent?

Accepted Answer

Yes, because $$P(A 	ext{ AND } B) = P(A) 	imes P(B)$$

Question 19

In a study, 408 out of 665 people are married. What is the probability that a randomly selected person is NOT married?

Accepted Answer

$$\frac{257}{665}$$

Question 20

Which of the following best describes conditional probability?

Accepted Answer

The probability of an event occurring given that another event has already occurred.

Probability and Conditional Probability: Study Notes for Introduction to Statistics (Lectures 7–13)

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