Question

15 POINTS!!!

Answer the question based on the data in the two-way table.

Below Above Total
Average Average
Boy 14 23 37
Girl 16 22 38
Total 30 45 75


Which statement is true?

A.
P(boy|above average grades) = P(boy)

B.
P(above average grades|boy) = P(above average grades)

C.
P(boy|above average grades) P(above average grades)

D.
P(above average grades|boy) = P(boy)

Answer 1

b...................

Answer 2

B.
`P(Above\ Average|Boy)=P(Above\ Average)`

Explanation:

We know that,

The conditional probability of event A, given event B is P(A|B), where,

`P(A|B)=(P(A\bigcap B))/(P(B))`.

Using the formula, we have,

`P(Boy|Above\ Average)=(P(Boy\bigcap Above\ Average))/(P(Above\ Average))\\\\P(Boy|Above\ Average)=(23)/(45)\\\\P(Boy|Above\ Average)=0.51`

And, we have,

`P(Above\ Average|Boy)=(P(Above\ Average\bigcap Boy))/(P(Boy))\\\\P(Above\ Average|Boy)=(23)/(37)\\\\P(Above\ Average|Boy)=0.6`

Since, the other probabilities are given by,

`P(Boy)=(37)/(75)=0.49`

`P(Above\ Average)=(45)/(75)=0.6`

So, we get that the correct option is,

B.
`P(Above\ Average|Boy)=P(Above\ Average)=0.6`