Answer to Question #122056 in Statistics and Probability for Ali khan

Question

In a Internee program at Airline Company, 60 percent of the internees are female and 40 percent
male. 80 percent of the females are business students, and 65 percent of the males are business
students.
a) An internee is selected at random. What is the probability that the person selected is a female
who is not a business student?
b) Are gender and field of study, independent in this case? Why?

Answer 1

Construct a contingency table from the information given

Gender/field of study Business non-business Total

Male 0.65*40=26 14 40

Female 0.80*60=48 12 60

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total 74 26 100

a) P(female but not business student)= 12/100=0.12

b) Gender and field of study are not independent.

Explanation :

condition for independent events:

P(A and B)=P(A)*P(B)

so for example, P(female and business student)=48/100=0.48

P(female)P(business student)= 60/100*74/100=0.444

since they are not equal, we say that gender and field of study are not independent.