Q: If two events A and B are independent, which formula correctly gives the probability that both A and B occur?

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

Q: A bag contains 5 red and 4 white marbles. A marble is drawn, replaced, and then another is drawn. What is the probability that the first is red and the second is white?

$$\frac{5}{9} \times \frac{4}{9}$$

Question 1

Suppose you roll two fair six-sided dice, one blue and one red. What is the probability that the sum of the numbers showing is 7?

Accepted Answer

$$\frac{1}{6}$$

Question 2

A jar contains 10 green, 12 blue, and 14 red marbles. If you randomly select one marble, what is the probability that it is blue?

Accepted Answer

$$\frac{12}{36}$$

Question 3

If the probability of rain today is 23%, what is the probability that it will NOT rain today?

Accepted Answer

$$0.77$$

Question 4

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot occur at the same time

Question 5

A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is a jack?

Accepted Answer

$$\frac{1}{13}$$

Question 6

Which probability approach is best for determining the probability of getting a 5 when tossing a fair die?

Accepted Answer

Classical approach

Question 7

If two events A and B are independent, which formula correctly gives the probability that both A and B occur?

Accepted Answer

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

Question 8

A car dealer has 200 cars: 85 black, 50 white, and 65 blue. What is the probability that a randomly selected car is black or white?

Accepted Answer

$$\frac{135}{200}$$

Question 9

A bag contains 5 red and 4 white marbles. A marble is drawn, replaced, and then another is drawn. What is the probability that the first is red and the second is white?

Accepted Answer

$$\frac{5}{9} 	imes \frac{4}{9}$$

Question 10

Which of the following is an example of independent events?

Accepted Answer

Owning a dog and growing your own herb garden

Question 11

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and A and B are mutually exclusive, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.9$$

Question 12

A single card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card is a club or a face card?

Accepted Answer

$$\frac{19}{52}$$

Question 13

An experiment consists of tossing a coin and then rolling a die. What is the probability that the coin lands heads up or the number is five?

Accepted Answer

$$\frac{1}{2} + \frac{1}{6} - \frac{1}{12}$$

Question 14

The Law of Large Numbers states that as an experiment is repeated many times, the relative frequency probability of an event:

Accepted Answer

Approaches the actual probability

Question 15

If the probability of team A winning is $$\frac{1}{3}$$, team B is $$\frac{1}{5}$$, and team C is $$\frac{1}{9}$$, what is the probability that either A or B wins?

Accepted Answer

$$\frac{8}{15}$$

Question 16

Which of the following is NOT a property of probability?

Accepted Answer

Probability can be negative

Question 17

A family has three children. What is the probability that exactly two of them are boys (assuming boys and girls are equally likely)?

Accepted Answer

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

Question 18

Which of the following best describes the empirical (relative frequency) approach to probability?

Accepted Answer

Based on the long-run proportion of times an event occurs in repeated trials

Probability: Basic Concepts, Rules, and Applications

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