coin tossing probability

Question

In a study, a researcher cites the problem of three coins, one of which is biased so that it turns up heads 65% of the time. If you randomly select one of the coins, toss it two times, and obtain two heads, what is the probability that this is the biased coin?

Answer 1

The sample space is:

 

Biased coin and 2 heads with probability = 1/3 * (.65)² = .14083333

Biased coin and not 2 heads with probability = 1/3 (1 - .1408333) = .1925

Unbiased coin and 2 heads = 2/3 * 1/4 = 1/6 = .1666666

Unbiased coin and not 2 heads = 2/3 * 3/4 = ,5

 

Event A = biased coin and event B = 2 heads

P(A|B) = P(A∩B)/P(B) = .14083333/(.14083333 + .16666) = .457995