Suppose you are invited to play a game in which you bet 1 on

Suppose you are invited to play a game in which you bet $1 on any number from 000 to 599.If your number comes up, you get $450.Find the expected winnings.

Solution

Given data:

Amount of bet on each number = $1

Total numbers 000 to 599 = 600

Reward on winning = $450

Therefore,

Expected winnings = Expected gained amount - Expected lost amount

Expected winnings = (Reward on winning -Amount per bet)*(Probability of winning) - (Amount per bet)*(Probability of losing)

Expected winnings = (450-1)*(1/600) - (1)(599/600)

Expected winnings = 449/600 - 599/600

Expected winnings = (449-599)/600 = -150/600

Expected winnings = -1/4 = -0.25

Expected winnings = $-0.25