You are attending a baseball game with two family members wh

You are attending a baseball game with two family members when it is announced that four fans in your section (which hols 20 spectators total) will win a free autographed baseball. A) what is the probability that at least one member of your family (including yourself) wins an autographed baseball? B) What is the probability that exactly two members of your family win an autographed baseball? C) What is the probability that all three of you win an autographed baseball?

--Please show how to do this with a Hypergeometric Distribution--

Solution

a)

P (x >= 1) = P(x=1 ) + P(x=2) + P(X=3)

P(x>=1 ) = [ 3C1 * 17C3 ] / 20C4   +      [3C2 * 17C2 ]   / 20C4    +   [3C3 * 17C1] / 20C4

P(x>=1 ) = 0.4211 + 0.0842 + 0.0035 = 0.5088

b)

P(X=2)= [3C2 * 17C2 ]   / 20C4 = 0.0842

c)

P(x=3)= [3C3 * 17C1] / 20C4 = 0.0035