# 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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