Question: Suppose that coin 1 has probability 0.6 of coming up heads, and coin 2 has probability 0.3 of coming up heads. If the coin flipped

Suppose that coin 1 has probability 0.6 of coming up heads, and coin 2 has probability 0.3 of coming up heads. If the coin flipped today comes up heads, then we select coin 1 to flip tomorrow. If the coin flipped today comes up tails, then we select coin 1 to flip tomorrow with probability 0.2 and select coin 2 to flip tomorrow with probability 0.8.

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

(b) What proportion of flips use coin 2 in the long run?

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