A recent study looked into the amount of debt accumulated by

A recent study looked into the amount of debt accumulated by recent college graduates. The study found that, among those with student loans,

4444%

said working during college affected their grades.

(a) Convert this statement into a conditional probability, including a short description of the associated sample space.

(b) What percentage of students working during college have student loans? Can you tell?

(a) Let

Requals={recent

college graduate},

Hequals={has

student loans}, and

Wequals={working

affected grades}.The conditional probability is P(

W

H

R

|

H

W

R

)equals=4444%. The sample space is

W

H

R

.

(b) Select the correct choice and, if necessary, fill in the answer box to complete your choice.

A.

There are

nothing%

of students working during college that have students loans.

B.

There is not enough information to know the percentage of students working during college that have student loans.

Solution

a. Statement of conditional probability: The probability that working during college affected students\' grades, given that the student took loan. The sample space is that of Recent College graduates, and among the students who took loans, 44.44% said that working during college affected their grades.

P(W | H) = 44.44%

Sample space : R

b. There is not enough information to know the percentage of students working during college that have student loans.

Because, we need the probability of students working during college and conditional probability of students who took loans given they work during college.