Conditional Probabilities of Events A and B

What are the conditional probabilities of events A and B?

Are A and B independent events?

Answer:

The conditional probabilities of the two events are; P(A|B) = 0.2 and P(B|A) = 0.25. The events are dependent.

Conditional probability is the likelihood of an event occurring given that another event has already occurred. In this case, the conditional probabilities of events A and B are calculated as follows:

P(A|B) = P(A ∩ B) / P(B)

P(A|B) = 3% / 15% = 0.2

P(B|A) = P(B ∩ A) / P(A)

P(B|A) = 3% / 12% = 0.25

Since the conditional probabilities are not equal, the events A and B are dependent on each other.

To determine if events A and B are independent, the formula P(A ∩ B) = P(A) * P(B) can be used. If the equation holds true, then the events are independent.

Independent events are events where the occurrence of one event does not affect the occurrence of the other event. In this case, the two events A and B are not independent as their probabilities are not independent of each other.