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Survey data indicate that 42% of customers at Mega Hit video rental stores subscribe to premium movie channels through their cable television provider. The data also indicate that 31% of MegaHit customers own a DVD player, while 56% of MegaHit customers subscribe to premium movie channels or own a DVD player (or both). What is the probability that a randomly selected Mega Hit customer both owns a DVD player and subscribes to premium movie channels? Write your answer as a decimal (not as a percentage). (If necessary, consult a list of formulas.) xs ?

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Answer:

P=0.17

Step-by-step explanation:

If A and B are dependent events, then we have a Rule of Addition:

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Let A represent event that customer at Mega Hit is subscribed to premium movie channels while B represent event that customer at Mega Hit owns a DVD, so, we get the following:

[tex]P(A)=0.42\\P(B)=0.31\\P(A \cup B)=0.56\\\\[/tex]

We need to find [tex]P(A \cap B)[/tex] or probability that a randomly selected Mega Hit customer both owns a DVD and subscribes to a premium movie channels.

Using Rule of Addition, we get:

[tex]0.56=0.42+0.31-P(A \cap B)\\\\0.56=0.73-P(A\cap B)\\P(A\cap B)=0.73-0.56\\P(A\cap B)=0.17[/tex]

So, the required probability is 0.17.

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