Question

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?

Answer 1

`Probability = 0.0435`

Step-by-step explanation:

Given

`p= 19\%` -- 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.

`q = 1 - p`

`q = 1 - 19\%`

`q = 81\%`

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:

`Probability = q^7*p`

`Probability = (81\%)^7*(19\%)`

`Probability = (0.81)^7*(0.19)`

`Probability = 0.81^7*0.19`

`Probability = 0.04346590566`

Approximate

`Probability = 0.0435`