Question

Q 2. There are two coins, one fair and one biased with P[H] = 0:4. 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 H, then the other coin is used on the next flip, and the result is noted. If the result of a flip is T, then the same coin is used on the next flip, and the result is noted.

(a) Formulate a Markov Chain model for this situation.( please outline what is involved in this part )

(b) Find the probability that the fourth flip is a head in the game above.

(c) Find the long-term probability that the flip is made with the biased coin. [7 marks each]

Answer 1

P(coin comes up H] = biased coin is selected and head t biased coin 2-selected and head f Fair is selected and head. = (1/3) *0.3 + (1/3) ^* 0.8 + (1/3) ^* (1/2) \r\n P(coin selected was the Fair one the given result is H) = P(Fair coin and head) /theta P(H comes = (1/3) *(1/2) /0.5333 = 0.3125