[tex]\text{probability}=\frac{\text{ number of favorable cases}}{\text{ total number of cases}}[/tex]
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:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
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:
[tex]P(A\cap B)=\frac{1879}{10730}[/tex]
The probability that a student is a graduate is:
[tex]P(B)=\frac{2610}{10730}[/tex]
Finally, the probability that a student on financial aid given that is a graduate is:
[tex]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\%}[/tex]
