Phantom coins

Level pending

Snehal has \(3\) biased coins labeled as \(A,B\) and \(C\). The probabilities that \(tail\) appears after they are flipped are given by \(P(A)=\frac{1}{2}\),\(P(B)=\frac{1}{4}\) and \(P(C)=\frac{1}{8}\) respectively. If all the coins are flipped simultaneously, then the probability that exactly \(2\) heads are obtained is given by \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

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