Advanced Placement (AP) College

At an electronics store, 19% of the customers who purchase a home theater system also pay for the professional installation that
the store offers. What is the probability that the eighth customer to buy a home theater system today will also be the first to pay for
the professional installation?

Answers

Answer 1

Answer:

[tex]Probability = 0.0435[/tex]

Explanation:

Given

[tex]p= 19\%[/tex] -- probability that a customer pays for professional installation

Required

Determine the probability that the 8th customer is the first to pay

First, we calculate the probability that a customer do not pay for installation.

Represent this with q.

[tex]q = 1 - p[/tex]

[tex]q = 1 - 19\%[/tex]

[tex]q = 81\%[/tex]

The question implies that the first 7 customers chose not to pay.

So, the event is represented as:

Event: q q q q q q q q p

And the probability is:

[tex]Probability = q^7*p[/tex]

[tex]Probability = (81\%)^7*(19\%)[/tex]

[tex]Probability = (0.81)^7*(0.19)[/tex]

[tex]Probability = 0.81^7*0.19[/tex]

[tex]Probability = 0.04346590566[/tex]

Approximate

[tex]Probability = 0.0435[/tex]

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