Suppose we select 12 face cards (a jack, a queen, and a king for each of the 4 suits) from a standard deck of cards. What is the probability of drawing 2 red Queens if 5 cards are drawn.

Question

a. 80/243

b. 20/243

c.33/90

d. 243/70

(Write (e.) if the answer is none among the choices.

Answer 1

This is not a binomial probability, it is a hypergeometric probability.

We select 2 out of 2 red queens, and 3 of the 10 remaining cards, in a sample of 5 of 12

In Excel, hypgeom.dist(2,5,2,12,0) = 5/33

Of course, we can also solve this using combinations.

This is

C(2,2)C(10,3)/C(12,5) = 1*120/792 = 5/33