A Coin Toss Problem

A fair coin is tossed repeatedly and the record of the outcomes is kept.

Now an event E is defined such that tossing of the coin is stopped when the total number of heads obtained so far exceeds the total number of tails by 3. For example, a possible sequence of tosses could look like \( HHTTTHTHHTHH\) .

What is the probability that the length of such a sequence is at most 10?

The answer is of the form \( \frac{a}{b}\) , Evaluate \(b-a\) .

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