Question

More than 40 million Americans are estimated to have at least one outstanding student loan to help pay college expenses ("40 Million Americans Now Have Student Loan Debt", CNNMoney, September 2014). Not all of these graduates pay back their debt in satisfactory fashion. Suppose that the following joint probability table shows the probabilities of student loan status and whether or not the student had received a college degree. If needed, round your answers to three decimal digits.

		College Degree
		Yes	No
Loan Status	Satisfactory	0.38	0.24	0.62
	Delinquent	0.16	0.22	0.38
		0.54	0.46

(a)	What is the probability that a student with a student loan had received a college degree?
(b)	What is the probability that a student with a student loan had not received a college degree?
(c)	Given that the student has received a college degree, what is the probability that the student has a delinquent loan?
(d)	Given that the student has not received a college degree, what is the probability that the student has a delinquent loan?
(e)	What is the impact of dropping out of college without a degree for students who have a student loan?
	- Select your answer -ObtainingNot obtainingItem 5  a college degree will lead to a greater probability of struggling to payback the student loan and will likely lead to financial problems in the future.

Answer 1

a)

Given table is

College Degree
		Yes	No	Total
Loan	Satisfactory	0.38	0.24	0.62
Status	Delinquent	0.16	0.22	0.38
Total		0.54	0.46	1

we have to find the probability that a student with a student loan had received a college degree

which is shown in table total of college degree "YES'"column

so probability will be 0.38+0.16=0.54

b)

we have to find the probability that a student with a student loan had not received a college degree

which is shown in table total of college degree "NO" column

so probability will be 0.24+0.22=0.46

c)

Given that the student has received a college degree, We have to find  the probability that the student has a delinquent loan

Applying the conditional probability

P(D/Y)= the probability that the student has a delinquent loan Given that the student has received a college degree

=Student has both degree and delinquent loan=0.16

P(Y)=that a student with a student loan had received a college degree=0.54

d)

Given that the student has not received a college degree, We have to Find the probability that the student has a delinquent loan

Applying the conditional probability

P(D/N)= the probability that the student has a delinquent loan Given that the student has not received a college degree

=Student has not  degree and delinquent loan=0.22

P(N)=that a student with a student loan had not received a college degree=0.46

e)

We have to find the impact of dropping out of college without a degree for students who have a student loan

students would not be able to repay the loan because he would be unable to earn money in future & he will face financial problems.