If A and B are independent, is this true? Why or why not?
P(A and B |C) = P(A|C) * P(B|C)
2026-03-30 07:07:55.1774854475
How to find intersection of two events dependant on another event?
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Consider tossing of two fair coins independently. Let $A$ be the event that both outcomes are Heads or both outcomes are Tails, $B$ the event that the first toss results in Heads and $C$ the event that the second toss results in Heads. Then you can verify that these events are pairwise independent but $\frac 1 4=P(A\cap B \cap C) \neq \frac 1 8= P(A)P(B)P(C)$. Your equation becomes $\frac {P(A\cap B \cap C)} {P(C)} =P(A)P(B)$. This is a contradiction.