In a sample of 1446 U.S. registered voters, 217 said that JFK was the best

Question

president since WWII. Two registered voters are selected at random without replacement.

(a) Find the probability that both registered voters say that JFK was the best.

(b) Find the probability that neither registered voters says that JFK was the best.

(c) Find the probability that at least one of the two registered voters says that JFK was the best president since WWII.

Answer 1

There are three ways of solving this: conditional probability, combinatorics, or the hypergeometric distribution (this is what this problem belongs to).

I will use the last, since it is the easiest and most appropriate.

Excel has this function, so I will assume that you can use it.

a) = hypgeom.dist(2,2,217,1446,0) 0.0224324828784333 (choose 2 JFK in a sample of 2 when 217 JFK in a sample of 1446; the final 0 means exact)

b) = hypgeom.dist(0,2,217,1446,0) 0.722294170291988

c) 1 - P(0) = 1 - 0.722294170291988 = 0.277705829708012