Discrete Random Variables we are working with commonly used

Discrete Random Variables
we are working with commonly used discrete and continuous distribution

In a hospital there are 16 patients, 4 of whom have AIDS. A doctor is assigned to 6 of these patients at random. What is the probability that he gets 2 of the AIDS patients?

Solution

There are 16C6 ways to choose any 6 patients.

There are 4C2 ways to get 2 with AIDS, and 12C4 to choose 4 without.

Thus,

P = [(12C4)(4C2)]/(16C6) = 0.370879121 [ANSWER]