Question

two balls are chosen randomly from an urn containing 5 white, 3 black, and 2 orange balls. suppose that you win $2 for each black ball selected and you lose $1 for each white ball selected. what is the expected amount you will win from this game

Answer 1

2.601

Explanation:

Given that:

White balls, W = 5

Black balls, B = 3

Orange balls, O = 2

Total = (5 + 3 + 2) = 10

Winning = $2 for each black ball chosen

Winning = - $1 for each white ball

Sample space for making 2 selections ; order does not matter :

{WW, WO, WB, OO, OB, BB}

WW __WO __WB __OO ___OB __BB

-2 ____ - 1 __ 1 ____ 0 ____ 2 ___ 4

WW = 5C2 / 10C2 = 0.2222

WO = (5C1 * 2C1) / 10C2) = 0.222

WB = (5C1 * 3C1) / 10C2) = 0.3333

OO = (2C2) / (10C2) = 0.0222

OB = ((2C1) * (3C1)) / 10C2 = 0.1333

BB = 3C2 / 10C2 = 0.0667

Expected winning = Σx * p(x)

(-2 * 0.222) + (-1 * 0.222) + (1 * 0.333) + (0 * 0.022) + (2 * 0.133) + (4 * 0.667)

= 2.601