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:
but apparently this is wrong, since I have to consider the fact that both coins are equally likely to be flipped originally. Therefore you would have:
of obtaining a head using coin one initially.
of obtaining tails using coin one initially.
of obtaining a head using coin two initially.
of obtaining tails using coin two initially.
The problem is that if I make a matrix using these values, they won't sum up to one; so I'm a little lost on what to do.