You have 1 fair coin and 1 coin with 2 heads. Given that the first flip was a heads what is the probability of getting another heads?
My Answer: P(2H|F=H) = P(2H|F=H, Biased Coin)*P(Biased Coin) + P(2H|F=H, Unbiased Coin)*P(Unbiased Coin) = 0.5 + 0.25 = 0.75. In my equation, F refers to the First Throw. But the answer is supposed to be 5/6 and I can't seem to understand how.
Edit: From Arthurs comment I get the following, however, I dont know if this is the correct method, despite getting the correct answer:
P(Biased|F=H) = 2/3.
P(2H|F=H) = P(2H|(Biased|F=H))*P(Biased|F=H) + P(2H|(Unbiased|F=H))*P(Unbiased|F=H) = (1*2/3) + (1/2 * 2/3) = 5/6.