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A and B are two events. Let P(A)=0.5 , P(B)=0.9 and P(A and B)=0.15 .
Which statement is true?



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(A) and P(B|A)=P(B) .

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

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

Respuesta :

Answer:

option-C

Step-by-step explanation:

we are given

Let P(A)=0.5

P(B)=0.9

P(A and B)=0.15

we know that

[tex]P(A|B)=\frac{P(Aand B)}{P(B)}[/tex]

now, we can plug values

[tex]P(A|B)=\frac{0.15}{0.9}[/tex]

[tex]P(A|B)=0.16666[/tex]

but we have

P(A)=0.5

we can see that both are not equal

[tex]P(A|B)\neq P(A)[/tex]

so, A and B are not independent

so, option-C........Answer


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