Question

A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?

Answer 1

Answer:

The probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is $1-(\frac{3}{4})^4\ or\ 0.68$

Step-by-step explanation:

Consider the provided information.

According to store records, approximately 1/4 of all customers who go to the service department ask for help finding an item.

That means 3/4 of all customers who go to the service department will not ask for help.

We need to find the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item.

Here, at least 1 means 1 or more than one customers can go to the service department.

Subtract the probability that no customers will go to service department with 1. This will gives us the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item.

This can be written as:

$P(X\geq 1)=1-P(X$

$P(X\geq 1)=1-\binom{4}{0}(\frac{1}{4})^0(\frac{3}{4})^4$

$P(X\geq 1)=1-(\frac{3}{4})^4\\P(X\geq 1)=0.68$

Hence, the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is $1-(\frac{3}{4})^4\ or\ 0.68$