Consider the midterm and final for a statistics class. suppose 13% of students earned an a on the midterm. of those students who earned an a on the midterm, 47% received an a on the final, and 11% of the students who earned lower than an a on the midterm received an a on the final. you randomly pick up a final exam and notice the student received an a. what is the probability that this student earned an a on the midterm? the end-goal is to find p(midterm = a|final = a).

There is a 38.97% probability that this student earned an A on the midterm.

Step-by-step explanation:

The first step is that we have to find the percentage of students who got an A on the final exam.

Suppose 13% students earned an A on the midterm. Of those students who earned an A on the midterm, 47% received an A on the final, and 11% of the students who earned lower than an A on the midterm received an A on the final.

This means that

Of the 13% of students who earned an A on the midterm, 47% received an A on the final. Also, of the 87% who did not earn an A on the midterm, 11% received an A on the final.

So, the percentage of students who got an A on the final exam is

To find the probability that this student earned an A on the final test also earned on the midterm, we divide the percentage of students who got an A on both tests by the percentage of students who got an A on the final test.

The percentage of students who got an A on both tests is:

The probability that the student also earned an A on the midterm is

There is a 38.97% probability that this student earned an A on the midterm.