Question

TotalUniversity DataReceiving Not ReceivingFinancial Aid Financial Aid42223898Undergraduates8120Graduates18797312610Total6101462910730What is the probability that a given student is onfinancial aid, given that he or she is a graduate?Rounded to the nearest percent, [? ]%

Answer 1

`\text{probability}=\frac{\text{ number of favorable cases}}{\text{ total number of cases}}`

Let's define

A: a student is on financial aid

B: a student is a graduate

We want to find P(A|B), that is, the probability of A given B, which is computed as follows:

`P(A|B)=(P(A\cap B))/(P(B))`

P(A∩B) means the probability of A and B at the same time. In this case, the probability that a student is on financial aid and is a graduate. From the table:

`P(A\cap B)=(1879)/(10730)`

The probability that a student is a graduate is:

`P(B)=(2610)/(10730)`

Finally, the probability that a student on financial aid given that is a graduate is:

`P(A|B)=((1879)/(10730))/((2610)/(10730))=(1879)/(10730)\cdot(10730)/(2610)=(1879)/(2610)=0.72\text{ or 72\%}`