Question

University DataNot ReceivingTotalReceivingFinancial AidFinancial AidUndergraduates422238988120Graduates18797312610Total6101462910730If you know that a student receives financial aid,what is the probability that the student is agraduate student?

Answer 1

Step-by-step explanation:

Given;

We are given table showing the total number of graduates and undergraduates. Also the table shows the total number receiving financial aid also those not receiving financial aid.

Required;

If we know that a student receives financial aid, then what is the probability that the student is a graduate student?

Step-by-step solution;

We are already given the the condition that the student receives financial aid. Therefore;

`financial\text{ }aid=6101`

The probability that the student is a graduate and receives financial aid is;

`P[graduate\cap financial\text{ }aid]=1879`

Therefore, if a student is chosen from the school, the probability that the student is a graduate student given that he or she receives financial aid is;

`\begin{gathered} P[graduate|financial\text{ }aid]=\frac{P[graduate\cap financial\text{ }aid]}{P[financial\text{ }aid]} \\ \\ =(1879)/(6101) \\ \\ =0.307982297984 \end{gathered}`

Expressed as percentage, this now becomes;

`\begin{gathered} Percentage=0.307982297984*100 \\ \\ Percentage=30.7982297984 \end{gathered}`

Therefore, we can round this off to the nearest whole number and we have;

ANSWER:

`Probability=31\%`