Question

Assume the probability that you will make a sale on any given telephone call is 0.13. Find the probability that you​ (a) make your first sale on the fifth​ call, (b) make your sale on the​ first, second, or third​ call, and​ (c) do not make a sale on the first three calls.

Answer 1

Answer:

We are given that  the probability that you will make a sale on any given telephone call is 0.13.

Probability of success i.e. sale = p = 0.13

Probability of failure i.e. no sale = q = 1-0.13=0.87

(a) make your first sale on the fifth​ call

We will use geometric distribution

The geometric distribution is a discrete distribution for n=0, 1, 2, ... having probability density function

$P(n)=p(1-p)^{n-1} = pq^{n-1}$

sale is made on 5 th call

So. substitute n = 5

$P(5)=(0.13)(0.87)^{5-1}$

$P(5)=0.0744$

The probability that you​ make your first sale on the fifth​ call is 0.0744

b)make your sale on the​ first, second, or third​ call

$P(1)+P(2)+P(3)$

$0.3414$

The probability that you​ make your sale on the​ first, second, or third​ call is 0.3414

​ (c) do not make a sale on the first three calls.

$1-(P(1)+P(2)+P(3))$

Using part b

$1-(0.3414)$

$0.6586$

The probability that you do not make a sale on the first three calls is

0.6586