Probability that a girl that scored an A on the test.

Question

A class consists of 55% boys and 45% girls. It is observed that 25% of the class are boys and scored an A on the test, and 35% of the class are girls and scored an A on the test.

If a student is chosen at random and is found to be a girl, the probability that the student scored an A is ___.

Answer 1

This can be solved using a contingency table:

	Scored an A	Did not score an A	Totals
Boys	25	30	55
Girls	35	10	45
Totals	60	40	100

G = stands for girls

A = stands for the event the student scored an A

P(G|A) = P(G∩A)/P(A) = 35/60 = .5833