You know that P(A)=0.25 and P(A ∩B)=0.20. What is P(B |A) if; (a) A and B are independent even

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You know that P(A)=0.25 and P(A ∩B)=0.20. What is P(B |A)...

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Key Concepts

Conditional Probability

Conditional probability is the probability of one event occurring given that another event has already occurred. The formula is defined as P(B|A) = P(A ? B) / P(A), where P(A ? B) is the probability that both events A and B occur, and P(A) is the probability that event A occurs.

Independent Events

Independent events are events where the occurrence of one event does not affect the probability of the other. For independent events, the conditional probability P(B|A) is equal to the probability of event B, and the intersection probability is given by P(A ? B) = P(A)P(B). In calculations where independence is assumed, one would use this property to find missing probabilities.

Dependent Events

Dependent events are events where the occurrence of one event affects the probability of the other. When events are dependent, the relationship P(A ? B) = P(A)P(B) does not hold, and the conditional probability must be computed directly using the formula P(B|A) = P(A ? B) / P(A). This formula remains valid regardless of the dependency between the events.

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