TXT me

Discrete Mathematics Level 5

You flip a fair coin several times.

Find the expected value for the number of flips you'll need to make in order to see the pattern TXT, where T is tails, and X is either heads or tails.

The expectation value can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

Clarification: You are looking for the pattern TTT or THT. i.e. You will keep flipping until you see one of those two patterns, then count the number of flips you made.

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