At a certain college, 47% of the students are female, and 21% of the students major in finance. Furthermore, 12% of the students both are female and major in finance.
(a) What is the probability that a randomly selected finance major is female?
(b) What is the probability that a randomly selected female student majors in finance?
For convenience let there be 100 total students
Look at the following two-way table :
Finance Non- Finance Total
Female 12 35 47
Male 9 44 53
21 79 100
(a) From the table, the probability that a finance major is female = 12 / [ 12 + 9 ] = 12/ 21 = 4/7
(b) The probability that a randomly selected female majors in finance = 12 / 47