Respuesta :
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 [tex]1-(\frac{3}{4})^4\ or\ 0.68[/tex]
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:
[tex]P(X\geq 1)=1-P(X<1)[/tex]
[tex]P(X\geq 1)=1-\binom{4}{0}(\frac{1}{4})^0(\frac{3}{4})^4[/tex]
[tex]P(X\geq 1)=1-(\frac{3}{4})^4\\P(X\geq 1)=0.68[/tex]
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 [tex]1-(\frac{3}{4})^4\ or\ 0.68[/tex]
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 0.68.
Step-by-step explanation:
GIven :
According to store records, approximately [tex]\frac{1}{4}[/tex] of all customers who go to the service department ask for help finding an item.
Solution :
According to given statement we can say that [tex]\frac{3}{4}[/tex] of all customers who go to the service department will not ask for help.
Now, 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
[tex]\rm P(X\geq 1) = 1 - P(X<1)[/tex]
[tex]\rm P(X\geq 1) = 1 - (\dfrac{1}{4})^0 (\frac{3}{4})^4[/tex]
[tex]\rm P(X\geq 1) = 1 - (\dfrac{3}{4})^4[/tex]
[tex]\rm P(X\geq 1)=0.68[/tex]
Therefore, 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 0.68.
For more information, refer the link given below
https://brainly.com/question/2561151?referrer=searchResults
