Compound Event Probabilities Quiz

What is the formula to calculate the probability of two independent events A and B both occurring?

• P(A and B) = P(A) * P(B)

• P(A and B) = P(A) - P(B)

• P(A and B) = P(A) + P(B)

• P(A and B) = P(A) / P(B)

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.3, what is the probability of both events A and B occurring if they are independent?

• 0.12

• 0.25

• 0.1

• 0.7

Define independent events in the context of probability.

• Events that do not affect each other's probabilities

• Events that are influenced by each other

• Events that always occur together

• Events that have a high probability of occurring

What is the formula to calculate the probability of two dependent events A and B both occurring?

• P(A) + P(B)

• P(A) / P(B)

• P(A) * P(B|A)

• P(A) - P(B)

If the probability of event A occurring is 0.6 and the probability of event B occurring given that event A has already occurred is 0.4, what is the probability of both events A and B occurring if they are dependent?

• 0.6 + 0.4 = 1.0

• 0.6 / 0.4 = 1.5

• 0.6 - 0.4 = 0.2

• 0.6 * 0.4 = 0.24

Define dependent events in the context of probability.

• Events that have no impact on each other

• Events that are completely unrelated to each other

• Events that always occur together

• Events where the outcome of one event affects the outcome of the other event.

A bag contains 5 red and 3 blue marbles. If two marbles are drawn without replacement, what is the probability of drawing a red marble followed by a blue marble?

• 5/8 * 3/8 = 15/64

• 5/8 * 3/8 = 15/64

• 5/8 * 3/8 = 15/64

• 5/8 * 3/7 = 15/56

A box contains 4 defective and 6 non-defective bulbs. If two bulbs are selected at random with replacement, what is the probability that both bulbs are non-defective?

• 0.36

• 0.25

• 0.64

• 0.50

Explain the concept of conditional probability in the context of dependent events.

• The concept of conditional probability states that the probability of an event A occurring, given that event B has already occurred, is denoted as P(A|B) and is calculated as P(A and B) / P(B), where P(A and B) is the probability of both events A and B occurring together, and P(B) is the probability of event B occurring.

• Conditional probability is calculated as P(A and B) * P(B).

• The probability of event A occurring is always independent of event B.

• The concept of conditional probability is irrelevant in the context of dependent events.

A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a heart and then drawing a spade if the first card is not replaced?

• 1/16

• 1/32

• 1/8

• 1/26