Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 & 3. If X denotes the sum of the numbers, then the expected value of X is...

Step-by-step solution

Total number of ways to draw 2 cards from 5 cards is ⁵C₂ = 10 . Let X be the sum of the numbers on the two drawn cards. The possible values of X are 2, 3, 4, 5 . The probabilities for each sum are: P(X = 2) = ²C₂ 10 = 1 10 P(X = 3) = ²C₁ ²C₁ 10 = 4 10 P(X = 4) = ²C₁ ¹C₁ + ²C₂ 10 = 3 10 P(X = 5) = ²C₁ ¹C₁ 10 = 2 10 The expected value E(X) is given by X P(X) : E(X) = 2 1 10 + 3 4 10 + 4 3 10 + 5 2 10 E(X) = 2 + 12 + 12 + 10 10 = 36 10 = 3.6 Answer: 3.6