To toss of a fair coin until 3 heads occur in a row.

The transition matrix is

$\displaystyle \left(\begin{array}{cccc}0.5&0.5&0&0\\0.5&0&0.5&0\ \0.5&0&0&0.5\\0&0&0&1\end{array}\right)$

Question1 : Why are the elements on first column, row 2 and 3, are not zeroes?

Will the following reasoning be correct?

I am thinking: if the state space is

{$\displaystyle a_{o},a_{1},a_{2},a_{3}$}, the first column must be

must be reserved for probability of the nth toss being a tail.

When the next toss is a Head, it proceeds to the next state; otherwise, it's back to column one.

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I posted this question on Sept 30, and I found my reasoning to be correct.

Case closed.