For two events A and B, suppose P(A) = 0.35, P(B) = 0.65, and P(B|A) = 0.35. Then A and B are independent.

Name: For two events A and B, suppose P(A) = 0.35, P(B) = 0.65, and P(B|A) = 0.35. Then A and B are independent.
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Question

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Two events A and B are independent if P(A and B) = P(A) * P(B). Given P(B|A) = 0.35, we find P(A and B) = P(A) * P(B|A) = 0.35 * 0.35 = 0.1225. Since P(A) * P(B) = 0.35 * 0.65 = 0.2275, which is not equal to 0.1225, A and B are not independent.

For Two Events a and B, Suppose P(A) = 0