In a large national population of college students 72 attend

In a large national population of college students, 72% attend four­ year institutions and the rest attend two­ year institutions. Males make up 46% of the students in the four­ year institutions and 55% of the student in the two­ year institutions.

a) Find the probability that a randomly selected student from this population of college students is both female andat a four­ year institution.

b) Find the probability that a randomly selected student from this population of college students is female.

c) Consider randomly selecting a female student from this population. What is the probability that she attends a two­ year institution?

Solution

Sol)

Let A be the event that attend four­ year institutions and P(A)=0.72

Let B be the event that attend two­ year institutions and P(B)=0.28

Now 46% of the male students in the four­ year institutions =P(M/A) =0.46

54% of the female students in the four­ year institutions =P(F/A) =0.54

Now 55% of the male students in the two­ year institutions =P(M/B) =0.55

45% of the female students in the ftwo year institutions =P(F/B) =0.45

A) probability that a randomly selected student from this population of college students is both female andat a four­ year institution is given by

P(A and F) =P(A) *P(F/A) =0.72*0.54 =0.389

B)

probability that a randomly selected student from this population of college students is female.

P(F) =P(A)*P(F/A)+P(B)*P(F/B) = 0.72 * 0.54+0.28*0.45 =0.51

C)

Consider randomly selecting a female student from this population. the probability that she attends a two­ year institution

probability that she attends a two­ year institution is

P(B/F) =P(F)*P(F/B) =0.51*0.45 =0.23