Question

A person works in a large home improvement store and approaches customers to tell them about the store’s carpet sale. He then asks them if they would like to talk to a sales representative. From past experience, the person has found that the probability of getting a “yes” is about 0.32. Find the probability that the person’s first “yes” will occur with the fifth customer.

Answer 1

Obtain the probability that the person’s first “yes” will occur with the fifth customer.

It is given that the probability that the person getting a “yes” in past experience is 0.32.

That is, P(yes) = 0.32.

 

The general formula for the geometric distribution is given below:

P(n) = p(1 – p)n-1

 

Substitute 0.32 for p, and 5 for n in the above equation.

P(5) = 0.32(1 – 0.32)5-1

        = 0.32(0.68)4

       = 0.068

 

Thus the probability that the person’s first “yes” will occur with the fifth customer is 0.068.

Thus the probability that the person’s first “yes” will occur with the fifth customer is 0.068.