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:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

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:

$P(A\cap B)=\frac{1879}{10730}$

The probability that a student is a graduate is:

$P(B)=\frac{2610}{10730}$

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

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