Assume that showing a car is a Bernoulli trial, and each time she shows a car,

there is a probability of 0.25 that the customer will buy the car. The
saleswoman has a goal of selling at least one car a week.

How many cars must she show so that the probability of her reaching her goal
is at least 0.99?

To find out how many cars the saleswoman must show so that the probability of reaching her goal is at least 0.99, we need to calculate the probability of not selling a car in a week and using this information to determine the number of trials required.

First, let's find the probability of not selling a car in a single trial. In this case, the probability of a customer not buying a car is 1 - 0.25 = 0.75.

Next, let's calculate the probability of not selling a car in a week. Since each showing of a car is considered an independent Bernoulli trial, we can use the probability of not selling a car in a single trial raised to the power of the number of trials. Let's assume the saleswoman needs to show "n" cars in a week:

Probability of not selling a car in a week = (0.75)^n

So, to find the number of cars the saleswoman must show, we need to solve the following inequality:

(0.75)^n ≤ 1 - 0.99

Now, we can solve this inequality to find the minimum value of "n" to satisfy the given condition.