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

.78 rounded to the nearest hudredth as asked in the orignal question. You are welcome! :)

Answer 2

A student is chosen at random and is found to be a girl, the probability that the student scored an A is 0.5865 or 58.65%

Explanation:

Given : 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.

To find : If a student is chosen at random and is found to be a girl, the probability that the student scored an A is ?

Solution :

Let B be event to choose boys and G be event to choose girls.

Let E be event to scored grade A.

We have given,

P(B)=55%=0.55

P(G)=45%=0.45

25% of the class are boys and scored an A on the test

`P(E/B)=(P(E\cap B))/(P(B))=(0.25)/(0.55)=0.45`

35% of the class are girls and scored an A on the test

`P(E/G)=(P(E\cap G))/(P(B))=(0.35)/(0.45)=0.78`

Using Baye's Theorem of probability

If a student is chosen at random and is found to be a girl, the probability that the student scored an A.

`P(G/E)=(P(E/G)* P(G))/(P(E/G)* P(G)+P(E/B)* P(B))`

`P(G/E)=(0.78* 0.45)/(0.78* 0.45+0.45* 0.55)`

`P(G/E)=0.5865`

`P(G/E)=58.65\%`

Therefore, A student is chosen at random and is found to be a girl, the probability that the student scored an A is 0.5865 or 58.65%