Select the correct answer. If A and B are dependent events, which of these conditions must be true? A. P (A and B) = P (A) + P (B) B. P (A and B) = P (B) P (A) C. P (B|A) = P (B) D. P (A|B) = P (A) E. P (B|A) P (B)

Option E

P (B|A) is not equal to P (B).

Explanation:

Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed. Also, Two events are said to be independent if occurrence of the first does not affects the outcome of the second so that the probability is not changed.

For independent events: P (A and B) = P (A) x P (B).

Recall that P (B|A) = P (A and B) / P (A)

= P (A) x P (B) / P (A) = P (B).

Therefore, for dependent events, P (B|A) is not equal to P (B).

I got option E for edmentum