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A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .6 and P(B) = .5. What is P(B|A)?

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JeanaShupp

Answer: [tex]P(B|A)=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Given Events :

A =  Next component brought in for repair is an audio component.

B= Next component is a compact disc player.

Also, P(A)=0.6   and P(B)=0.5

Since B is contained in A.

So, A∩B = B

Then, P(A∩B)=P(B) = 0.5

Conditional probability formula :

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

Substitute values , we get

[tex]P(B|A)=\dfrac{0.5}{0.6}=\dfrac{5}{6}[/tex]

Hence, [tex]P(B|A)=\dfrac{5}{6}[/tex]

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