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?
Answers
Given:
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.
To find:
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?
Solution:
From given, we have,
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.
The condition for independent events:
P(A and B) = P(A) × P(B)
P(female and business student) = 48/100 = 0.48
P(female)P(business student) = 60/100 × 74/100 = 0.444
Since the probabilities are not equal, we say that gender and field of study are not independent.