Question

A class consists of 55% boys and 45% girls. It is observed that 25% of the class are boys and scored an A on the test, and 35% of the class are girls and scored an A on the test. If a student is chosen at random and is found to be a girl, the probability that the student scored an A is .

Answer 1

`P(A | B)=(7)/(9)=0.778`

Explanation:

Let's call B the event that consists of the selected student being a girl

Call A to the event in which the selected student obtained an A.

Then we look for the probability that A will occur given that B. That is, we look for P(A | B)

This is a conditional probability and is calculated using the following formula

`P(A | B)=(P(A\ and\ B))/(P(B))`

In this case

`P(B)=0.45\\P(A\ and\ B)=0.35`

So

`P(A | B)=(0.35)/(0.45)`

`P(A | B)=(7)/(9)=0.778`

Answer 2

The probability that the student scored an A is : 0.778

Explanation:

There are 55% boys and 45% girls

So, No of boys is: 55/100

No of girls is: 45/100

So, total no of girls are: 45

Since 35% of the girls scored A on test

No of girls who scored A on test = 35

The probability that the student scored an A is: 35/45

The probability that the student scored an A is : 0.778