Answer:
0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan
Step-by-step explanation:
The customers are chosen without replacement, which means that we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7D%2AC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
50 major customers, 15 would accept the plan.
This means that ![N = 50, k = 15](https://tex.z-dn.net/?f=N%20%3D%2050%2C%20k%20%3D%2015)
The utility selects 10 major customers randomly (without replacement) to contact and promote the plan.
This means that ![n = 10](https://tex.z-dn.net/?f=n%20%3D%2010)
a. What is the probability that exactly two of the selected major customers accept the plan
This is P(X = 2).
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7D%2AC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
![P(X = 2) = h(2,50,10,15) = \frac{C_{15,2}*C_{35,8}}{C_{50,10}} = 0.2406](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20h%282%2C50%2C10%2C15%29%20%3D%20%5Cfrac%7BC_%7B15%2C2%7D%2AC_%7B35%2C8%7D%7D%7BC_%7B50%2C10%7D%7D%20%3D%200.2406)
0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan