Police know that the crime was committed by one of the two suspects, A and B, with equal evidence against them initially. Further investigation suggests that the blood type of the guilty is found in 1/10 of the population. If A’s blood matches this type, whereas B’s is unknown, what is the probability that A is guilty?
The probability that A is guilty, given his blood matches = P(A|M)
P(A|M) = P(M|A) x P(A) /(P(M|A) x P(A) + P(M|B) x P(B))
P(A|M) = 1 x (1/2) /[1 x (1/2) + (1/10)x (1/2)] = 10/11
