Joe is considering pursuing an MBA degree.He has applied to two different universities.The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B.Is the acceptance decision at University A independent of the acceptance decision at University B?
A)Yes
B)No
$P(\text { Accept at } A)=.25=P(\text { Accept at } A \mid \text { Re ject at } B)=\frac{(.25)(.60)}{.60}=\frac{.15}{.60}=.25$

Question

Quizplus · Accepted Answer

The acceptance decision at University A is independent of the acceptance decision at University B. This is because the probability of acceptance at University A is the same regardless of whether or not Joe is accepted to University B. The calculation above shows that the probability of acceptance at University A given rejection at University B is the same as the overall acceptance rate at University A. Therefore, the decision at each university is independent of the decision at the other university.