A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green balls drawn and E(X) = 1.2 , then N =

Step-by-step solution

Total number of balls = N + 8 Two balls are drawn at random. Let X be the number of green balls drawn. The possible values of X are 0, 1, 2 . P(X=1) = ^ N C₁ ⁸C₁ ^ N+8 C₂ = 16N (N+8)(N+7) P(X=2) = ^ N C₂ ^ N+8 C₂ = N(N-1) (N+8)(N+7) The expected value E(X) is given by: E(X) = 1 P(X=1) + 2 P(X=2) E(X) = 16N + 2N(N-1) (N+8)(N+7) = 2N(N+7) (N+8)(N+7) = 2N N+8 Given E(X) = 1.2 , we have: 2N N+8 = 1.2 2N = 1.2N + 9.6 0.8N = 9.6 N = 12 Answer: 12