Question

In a finance class, the final grade is based on three tests. Historically, the instructor tells the class that the joint probability of scoring "A"'s on the first two tests is 0.5. A student assigns a probability of 0.9 that she will get an "A" on the first test. What is the probability that the student will score an "A" on the second test given that she scored an "A" on the first test?

Answer 1

D-- 0.44
P(A on the 2nd | A on the 1st) = P(A1 and A2)/P(A1) = .4/.9 = .44

Answer 2

The probability of getting an A on the second test given that she scored an A on the first test is
`P(A_1\&A_2)/P(A_1)=5/9\approx0.555`.

Explanation:

We assume that:

- The probability of getting A's in both exams is P=0.5.

- The probability of gettina an A in the first exam is P=0.9.

The probability of getting an A on the second test given that she scored an A on the first test can be calculated as:

`P(A_1\&A_2)=P(A_1)*P(A_2|A_1)\\\\P(A_2|A_1)=P(A_1\&A_2)/P(A_1)=0.5/0.9=0.555`