There are two coins, one fair and one biased (the probability of obtained a tails being...
There are two coins, one fair and one biased (the probability of obtained a tails being 0.2 - i.e., P[T] = 0:2). A game is played by successively flipping the coins as follows:
The game begins with a flip of the fair coin, and the result, H or T, is noted;
If the result of the flip is T, then the other coin is used on the next flip, and the result is noted;
If the result of a flip is H, then the same coin is used on the next flip, and the result is noted.
(a) Formulate a Markov Chain model for this situation.
(b) Find the probability that the eighth flip is a head in the game above.
(c) Find the long-term probability that the flip is made with the biased coin.
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