Question

The probability that a student graduating from Suburban State University has student loans to pay off after graduation is 0.60 The probability that a student graduating from this university has student loans to pay off after graduation and is a male is 0.12. Find the conditional probability that a randomly selected student from this university is a male given that this student has student loans to pay off after graduation.

Answer 1

The conditional probability  of a student selected is a male and has student loans to pay off after graduation in the State University is computed as follows: Given probabilities:

.12-  male with a loan to pay off after graduation (Event A)

.60 - male and female with a loan to pay off after graduation (Event B)

A/B

(.12)/.60

.2

Answer 2

Answer: probability that a randomly selected student from this university is a male given that this student has student loans to pay off after graduation. is P = 0.20

Step-by-step explanation:

Suppose you have two events A and B.

If the probability of event A is Pa, and the probability of event B is Pb, then the probability of both events to happen is equal to P = Pa*Pb.

In this case, we have that the probability for a student to have to pay a loan is 0.60

and the probability for the student to hate to pay a loan and also being a male is 0.12

then if being a male is event A, and having a loan is event B, we have:

Pa = ?

Pb = 0.60

P = Pa*Pb = 0.12

then we can obtain Pa as:

Pa*0.60 = 0.12

Pa = 0.12/0.60 = 0.20