Question

) The manager of a local Gap store estimates that on average the probability of a customer entering the store and will purchase something is 20% (0.20). Assume a Binomial distribution. 1. What is the probability that 3 of the next 4 customers will make a purchase? 2. What is the probability that none of the next 4 customers will make a purchase

Answer 1

Answer: 1. 0.0256

2. 0.4096

Step-by-step explanation:

Binomial probability formula , to find the probability of getting x successes:

$P(x)=^nC_xp^x(1-p)^{n-x}$ , where n= Total number of trials

p= Probability of getting success in each trial.

Let x be the number of customers will make purchase.

As per given , we have

p= 0.20

n= 4

1. The probability that 3 of the next 4 customers will make a purchase will be:-

$P(x=3)=^4C_3(0.20)^3(1-0.20)^{4-3}$

$P(x=3)=(4)(0.20)^3(0.80)^{1}\ \ [\because\ ^nC_{n-1}=n]$

$P(x=3)=(4)(0.008)(0.80)=0.0256$

Hence, the probability that 3 of the next 4 customers will make a purchase = 0.0256

2. The probability that none of the next 4 customers will make a purchase will be :

$P(x=0)=^4C_0(0.20)^0(1-0.20)^{4-0}$

$P(x=0)=(1)(0.80)^{4}\ \ [\because\ ^nC_{0}=1]$

$P(x=0)=0.4096$

Hence, the probability that none of the next 4 customers will make a purchase= 0.4096