If P(A|B) = 0.6, what is P(A^c|B)?

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Multiple Choice

If P(A|B) = 0.6, what is P(A^c|B)?

Explanation:
When we condition on B, A and its complement A^c are the two possibilities that can occur within B. They are mutually exclusive and together cover all outcomes under B, so their conditional probabilities must add up to 1. This gives the relation P(A^c|B) = 1 − P(A|B). With P(A|B) = 0.6, we get P(A^c|B) = 0.4. The other values would contradict this complementary relationship or imply impossible outcomes once B has occurred.

When we condition on B, A and its complement A^c are the two possibilities that can occur within B. They are mutually exclusive and together cover all outcomes under B, so their conditional probabilities must add up to 1. This gives the relation P(A^c|B) = 1 − P(A|B). With P(A|B) = 0.6, we get P(A^c|B) = 0.4. The other values would contradict this complementary relationship or imply impossible outcomes once B has occurred.

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