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**lllll** Coin 1 has probability of coming up heads with probability 0.7.

Coin 2 has probability of coming up heads with probability 0.6.

If we flip a coin today and it comes up heads, we will be flipping coin 1 tomorrow.

If we flip a coin today and it comes up tails ,we will be flipping coin 2 tomorrow.

if the coin initially flipped is equally likely to be coin 1 or coin 2, what is probability that the coin flipped on the third day after the initial flip is coin 1?

I'm having trouble setting my matrix, I was pretty sure that my matrix would look like:

$\displaystyle \begin{bmatrix}0.7 & 0.3\\0.6& 0.4\end{bmatrix}$

but apparently this is wrong, since I have to consider the fact that both coins are equally likely to be flipped originally. Mr F says: The transition matrix is $\displaystyle {\color{red}\begin{bmatrix}0.6 & 0.7\\0.4& 0.3\end{bmatrix}}$. The initial state matrix is $\displaystyle {\color{red}\begin{bmatrix}0.5 \\ 0.5 \end{bmatrix}}$. The final state matrix is $\displaystyle {\color{red}\begin{bmatrix}Pr(C1) \\ Pr(C1') \end{bmatrix}}$.

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