Probability Distributions

Question

	A	B	C	Total
Male	10	20	2	32
Female	16	3	5	24
Total	26	23	7	56

A test was given to a group of students. The grades and gender are summarized above

If one student is chosen at random from those who took the test, Find the probability that the student was female GIVEN they got a 'B'.

Answer 1

Conditional probabilities are the probability of A and B occurring together, given that B has occurred P(A|B). They are calculated as the probability of both events occurring together P(A∩B) divided by the probability of the GIVEN event P(B), or in this case the probability of selecting a girl that received a B grade (3/56) divided by the probability of selecting a girl (24/56).

So the answer is (3/56)/(24/56) = 3/24 = 1/8 or (0.125)