The academic register compiled data on 11 000 students which were summarized in a contingency table. The survey results were cross-classified by sex and faculty.
SEX
SCIENCE (S)
HUMANITIES (H)
BUSINESS (B)
ARTS (A)
TOTAL
Male (M)
2900
1200
1500
500
6100
Female(F)
2500
1100
1000
300
4900
Total
5400
2300
2500
800
11000
Suppose that the student is randomly selected what is the probability that the student is female if it is known that she is a business student?
0.3
0.55
0.68
0.4
To find the probability that a randomly selected student is female given that she is a business student, we need to use the formula for conditional probability:
P(Female | Business) = P(Female and Business) / P(Business)
From the contingency table, we see that the number of female business students is 1000. The total number of business students is 2500.
So,
P(Female | Business) = 1000 / 2500 = 0.4
Therefore, the probability that a randomly selected student is female, given that she is a business student, is 0.4.