A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag without replacement. Let X be the number of white balls drawn. If a player receives a reward of 10(X^2 - X) rupees, then the expected reward of the player (in rupees) is _________

Step-by-step solution

Let X be the random variable representing the number of white balls drawn in a sample of 3 balls from a total of 10 balls ( 4 white, 6 black). The probability of drawing exactly k white balls is given by P(X=k) = ⁴C_ k ⁶C_ 3-k ¹⁰C₃ . The possible values for X are 0, 1, 2, 3 . P(X=0) = ⁴C₀ ⁶C₃ ¹⁰C₃ = 1 20 120 = 20 120 P(X=1) = ⁴C₁ ⁶C₂ ¹⁰C₃ = 4 15 120 = 60 120 P(X=2) = ⁴C₂ ⁶C₁ ¹⁰C₃ = 6 6 120 = 36 120 P(X=3) = ⁴C₃ ⁶C₀ ¹⁰C₃ = 4 1 120 = 4 120 The expected reward is E[10(X^2 - X)] = 10 _ k=0 ³ (k^2 - k) P(X=k) . For k=0