contestada

A and B are two events. Let P(A)=0.8 , P(B)=0.4 and P(A and B)=0.32 . Which statement is true?

A and B are independent events because P(A|B)=P(A) .

A and B are independent events because P(A|B)=P(B) and P(B|A)=P(A) .

A and B are not independent events because P(A|B)=P(B|A) .

A and B are independent events because P(A|B)=P(B|A) .

Respuesta :

LammettHash
Since [tex]P(A)=0.8[/tex] and [tex]P(B)=0.4[/tex], we have [tex]P(A)\cdot P(B)=0.32=P(A\cap B)[/tex], which means [tex]A[/tex] and [tex]B[/tex] are independent events.

Because they are independent, we have

[tex]P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=P(A)[/tex]

so the first statement is true.

A and B are independent events because P(A∣∣B) = P(A) .

I just took the test :)

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