Question

4.98
Pollution control regulations. A task force established
by the Environmental Protection Agency was scheduled
to investigate 20 industrial firms to check for violations
of pollution control regulations. However, budget
cutbacks have drastically reduced the size of the task force,
and they will be able to investigate only 3 of the 20 firms. If
it is known that 5 of the firms are actually operating in violation
of regulations, find the probability that
a. None of the three sampled firms will be found in violation
of regulations.
b. All three firms investigated will be found in violation
of regulations.
c. At least 1 of the 3 firms will be operating in violation of
pollution control regulations.
Please do step by step ! there are some solutions to this question in here but it doesn't look right to me .

Answer 1

Probability of a firm which is randomly chosen operating in violation = 5/20 = 1/4 = 0.25

It is a binomial probability distribution with p = 0.25 and number of trials being 3.

a) P(X = 0) = 3C0*(0.25)⁰*(0.75)³ = 0.4219

b) P(X=3) = 3C3*(0.25)³*(0.75)⁰ = 0.0156

c) P(X>=1) = 1 - P(X=0) = 1 - 0.4219 = 0.5781