Inside two heads

Discrete Mathematics Level 3

Consider the following experiment : You are given 4 coins. You toss them simultaneously and you get some sequence of heads and tails.
Then you remove one of the coins and toss the remaining three coins.
Finally remove one more coin and toss remaining two coins.

The probability that in each of these three steps, you get at most 2 heads can be written as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime integers. What is the value of \(a+b\) ?

I created this problem with the help of my friend Pankaj.

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