Question

A representative of a market research firm contacts consumers by phone in order to conduct surveys. The specific consumer contacted by each phone call is randomly determined. The probability that a phone call produces a completed survey is 0.25. Calculate the probability that more than three phone calls are required to produce one completed survey.

Answer 1

Answer: 0.421875

Explanation:

According to the geometric distribution,

The probability that x number of trials take place until the first success occurs will be

`P(X=x)=(q)^(x-1)p`, where p is the probability of getting success in each trial.

Given : The probability that a phone call produces a completed survey is p=0.25.

then q=1-0.25=0.75

Now, the probability that more than three phone calls are required to produce one completed survey :

`P(X>3)=1-P(X\leq3)\\\\=1-(P(1)+P(2)+P(3))\\\\=1-((0.75)^(1-1)(2.5)+(0.75)^(2-1)(2.5)+(0.75)^(3-1)(2.5))=0.421875`

Hence, the probability that more than three phone calls are required to produce one completed survey = 0.421875