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 male if it is known that he studies humanities?
To find the probability that the student is male given that he studies humanities, we need to look at the row for humanities in the contingency table:
Total Male students in Humanities = 1200
Total students in Humanities = 2300
Therefore, the probability that a randomly selected student is male given that they study humanities is:
\( \frac{1200}{2300} = \frac{12}{23} \)
So, the probability that the student is male if it is known that he studies humanities is \( \frac{12}{23} \).