Twenty corporations were asked whether or not they provide r

Twenty corporations were asked whether or not they provide retirement benefits to their employees. fourteen of the corporations said they do provide retirement benefits to their employees, and 6 said they do not. five corporations are randomly selected from these 20. find the probability that

a) exactly 2 of them provide retirement benefits to their employees.

b) none of them provides retirement benefits to their employees.

c) at most one of them provides retirement benefits to employees.

Solution

number of corporation to agree = 14

probability agree = p = 14/20 = 0.7

q = 1 - p = 0.3

n=5

P(x=2) = nCr p^2 q^3

P(x=2) = 5C2 * 0.7^2 * 0.3^3

P(x=2) = 0.1323

2

P(x=0) = 5C0 * p^0 q^5

P(x=0) = 5C0 * 0.7^0 * 0.3^5

P(x=0) = 0.00243

3.

at most one mean either zero or one

P(x<=1) = P(x=0) + P(x=1)

P(x<=1) = 0.00243 + 5C1 * 0.7 *0.3^4

P(x<=1) = 0.03078