Question

Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 and 3. Let X denote the sum of numbers. Find expected value of the sum.

Answer 1

Let S be the sample space.

∴ S = {(1, 1), (1, 2), (1, 3), (2, 2), (2, 3)}

Let X = sum of numbers on cards.

∴ X = 2, 3, 4

X	2	3	4	5
P(x)	`1/5`	`1/5`	`2/5`	`1/5`

E(X) = `sumx_i * P(x_i)`

= `2 xx 1/5 + 3 xx 1/5 + 4 xx 2/5 + 5 xx 1/5`

= `18/5`

= 3.6