If A and B are independent events with P(A)=0.5 and P(B)=0.4, what is P(A|B)?

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Multiple Choice

If A and B are independent events with P(A)=0.5 and P(B)=0.4, what is P(A|B)?

Explanation:
When two events are independent, the occurrence of one does not change the probability of the other. So the conditional probability P(A|B) equals P(A). Compute using the definition: P(A|B) = P(A ∩ B) / P(B). For independent events, P(A ∩ B) = P(A)P(B) = 0.5 × 0.4 = 0.2. Then P(A|B) = 0.2 / 0.4 = 0.5. This result shows that knowing B occurred leaves A’s probability unchanged at 0.5. The other numbers would come from non-conditional quantities (like P(A ∩ B) = 0.2 or P(B) = 0.4), which aren’t the conditional probability.

When two events are independent, the occurrence of one does not change the probability of the other. So the conditional probability P(A|B) equals P(A).

Compute using the definition: P(A|B) = P(A ∩ B) / P(B). For independent events, P(A ∩ B) = P(A)P(B) = 0.5 × 0.4 = 0.2. Then P(A|B) = 0.2 / 0.4 = 0.5.

This result shows that knowing B occurred leaves A’s probability unchanged at 0.5. The other numbers would come from non-conditional quantities (like P(A ∩ B) = 0.2 or P(B) = 0.4), which aren’t the conditional probability.

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