Topic 12: Probability of Independent Events

Two dice are rolled. What is the probability that both dice show a 6?

A coin is flipped and a die is rolled. What is the probability of getting a head on the coin and a 4 on the die?

Which of the following pairs of events are independent?

• Drawing two cards from a deck without replacement

• Flipping a coin and rolling a die

• Drawing two cards from a deck with replacement

• Both B and C

If the probability of event X is 0.5 and the probability of event Y is 0.2, what is the probability of both X and Y occurring if they are independent?

• 0.1

• 0.3

• 0.5

• 0.7

A bag contains 3 red balls and 2 blue balls. If two balls are drawn with replacement, what is the probability that both are red?

A spinner has 4 equal sections colored red, blue, green, and yellow. What is the probability of landing on red and then blue in two spins?

• 0.1

• 0.3

• 0.5

• 0.6

A jar contains 5 white marbles and 3 black marbles. If two marbles are drawn with replacement, what is the probability that both are black?

Which of the following statements is true about independent events?

• The occurrence of one event affects the occurrence of the other.

• The probability of both events occurring is the sum of their probabilities.

• The probability of both events occurring is the product of their probabilities.

• The events cannot occur simultaneously.