Question

Find P(AIA^c) A. 1 B. 0 C. 1/2 D. unknown Please select the best answer from the choices provide

Answer 1

By definition of conditional probability,

$\mathbb P(A\mid A^C)=\dfrac{\mathbb P(A\cap A^C)}{\mathbb P(A^C)}$

But any event and its complement cannot occur simultaneously; they are disjoint, so the probability of their intersection is 0. So the conditional probability is also 0.