Yes I need points so I’m commenting random stuff lolololo
Using the binomial distribution, it is found that there is a 0.81 = 81% probability that NEITHER customer is selected to receive a coupon.
For each customer, there are only two possible outcomes, either they receive the coupon, or they do not. The probability of a customer receiving the coupon is independent of any other customer, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- For each customer, 10% probability of receiving a coupon, thus
. - 2 customers are selected, thus
![n = 2](https://tex.z-dn.net/?f=n%20%3D%202)
The probability that <u>neither receives a coupon is P(X = 0)</u>, thus:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{2,0}.(0.1)^{0}.(0.9)^{2} = 0.81](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B2%2C0%7D.%280.1%29%5E%7B0%7D.%280.9%29%5E%7B2%7D%20%3D%200.81)
0.81 = 81% probability that NEITHER customer is selected to receive a coupon.
A similar problem is given at brainly.com/question/25326823