Here is another problem with conditional probability. There are three men and two women. If one of the men is a carpenter, what is the probability of randomly selecting a carpenter and a man from the group?
Let M represent man, W represents woman, and C represents carpenter.
P(M AND C) = P(M) x P(C|M)
The probability of choosing a man is 3 in 5; the probability that it’s a carpenter, given a man is chosen, is 1/3
= 3/5 x 1/3 = 1/5
This can also be done the following way
P(C AND M) = P(C) x P(M|C)
The probability of choosing a man is 1 in 5; the probability that it’s a man, given it’s a carpenter, is 100%.
= 1/5 x 1 = 1/5
