Answer to Question #166836 in Statistics and Probability for Eliza

Question

Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Find the values of the random variable Z.

Answer 1

3 options are possible:

1. Z = 0; P(Z = 0) = C²₅*C⁰₆/C²₁₁ = (5!/(2!*(5-2)!))/(11!/(2!*(11-2)!)) = 10/55 = 2/11

2. Z = 1; P(Z = 1) = C¹₅*C¹₆/C²₁₁ = (5!/(1!*(5-1)!))*(6!/(1!*(6-1)!))/(11!/(2!*(11-2)!)) = 30/55 = 6/11

3. Z = 2; P(Z = 2) = C⁰₅*C²₆/C²₁₁ = (6!/(2!*(6-2)!))/(11!/(2!*(11-2)!)) = 15/55 = 3/11