a county welfare agency employees 30 welfare workers who int

a county welfare agency employees 30 welfare workers who interview prospective food stamp recipients. periodically, the supervisor selects, at random, the forms completed by two workers to audit for illegal deductions. Unknown to the supervisor, 8 of the workers have regularly been given illegal deductions to all applicants. what is the probability both workers chosen have been given illegal deductions? round to the nearest thousandth.

Solution

Answer to the question)

Out of 24 workers , 9 are working illegally

Thus Probability of illegal (p) =9/24 = 0.3750

.

Total number of people selected n = 2

we need to find the probabiltiy that both are wrokign illegal , this implies that x = 2

.

This is a problem of binomial probability

the formula is as follows:

P(X=x) = nCx * p^x * (1-p)^n-x

.

On plugging the values we get

P(x=2) = 2C2 * (0.3750)^2 * 0.625^0

P(x=2) = 1* 0.140625 * 1

P(x=2) = 0.140625