Phantom coins

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 $a+b$ ?