Topic:Conditional Probability
For any two events A and B, where P(B) ≠ 0, P( A | B ) = P( A ∩ B ) / P( B ) = P( B | A) * P(A) / P(B)..i.e..{the probability of A given B is equal to the probability of A and B divided by the probability of B}
For a set of events A1, A2, A3, ... , An,
hence,
P(B)
= P(B and A1) + P(B and A2) + ... + P(B and An)
= P(B | A1) * P(A1) + P(B | A2) * P(A2) + ... + P(B | An) * P(An)
P(M | N)
= P(N | M) * P(M) / P(N)
= P(N | M) * P(M) / (P(N | M) * P(M) + P(N | M') * (1 - P(M)))
Substitute Values.... you get ?
