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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)

Respuesta :

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

Answer:

B. [tex]P(Above\ Average|Boy)=P(Above\ Average)[/tex]

Step-by-step explanation:

We know that,

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

[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex].

Using the formula, we have,

[tex]P(Boy|Above\ Average)=\dfrac{P(Boy\bigcap Above\ Average)}{P(Above\ Average)}\\\\P(Boy|Above\ Average)=\dfrac{23}{45}\\\\P(Boy|Above\ Average)=0.51[/tex]

And, we have,

[tex]P(Above\ Average|Boy)=\dfrac{P(Above\ Average\bigcap Boy)}{P(Boy)}\\\\P(Above\ Average|Boy)=\dfrac{23}{37}\\\\P(Above\ Average|Boy)=0.6[/tex]

Since, the other probabilities are given by,

[tex]P(Boy)=\dfrac{37}{75}=0.49[/tex]

[tex]P(Above\ Average)=\dfrac{45}{75}=0.6[/tex]

So, we get that the correct option is,

B. [tex]P(Above\ Average|Boy)=P(Above\ Average)=0.6[/tex]

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