For two events, M and N, P (M) = 0.7, P (N|M) = 0.3, and P (M'|N')

Topic:C onditional 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?