Let A and B be two events such that = , P(A ∩ B) = and P() = , where stands for the complement

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Let A and B be two events such that = , P(A &#8745; B) = and P() = , where stands for the complement of the event A. Then the events A and B are

Accepted Answer

= &#8658; P(A &#8746; B) = 1- P() = &#8658; P(A) = 1 - &#8757; P(A &#8746; B) = P(A)+ P(B) - P(A &#8745; B) + P(B) - P(B) = &#8757; P(A) &#8800; P(B) so they are not equally likely. Also P(A) &#215; P(B) = P(A &#8745; B) &#8757; P(A &#8745; B) = P(A).P(B) so A & B are independent.

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