There are 30 restaurants in a certain town. Assume that four of them have health code violations. A health inspector chooses 10 restaurants at fandom to visit.

a. What is the probability that two of the restaurants with health code violations will be visited?

b. What is the probability that none of the restaurants that are visited will have health code violations?

Answer :

Step 1 of 3:

Given, a health inspector chooses 10 restaurants at random in a 30 restaurants in a certain town.

We have to assume that four of them have health code violations.

Let X follows Hypergeometric distribution with probability mass function is

P(x) =

Where, N = 30, n = 10 and k = 4

Step 2 of 3:

The claim is to find the probability that two of the restaurants with health code violations will visited.We have to find P(x=2)

Then, P(x=2) =

=

=

= 0.312

Hence, the probability that two of the restaurants with health code violations will visited is 0.312