Question

I am going to play a game of chance, but I want to know if it is worth my while. On average, if I played the game over and over, what amount would I expect to win (+$) or lose (-$) on average per game? That is the mean of the probability distribution that describes the game. It is also call the game's expected value.

The formula for expected value is

The game I'm playing costs $5 to play. The jackpot I'd win is $100,000

I have 23,500 ways to make an entry, but only one of these will win the jackpot.

What is the expected value of this game, rounded to the nearest cent?

Be sure to include a - sign if the expected value is negative. Enter your solution as a number in dollars and cents, for example, 1.34 or -0.23.

Answer 1

Probability of win = 1/23500

Probability of loss = 1 - 1/23500 = 23499/23500

Winning amount = 100000 - 5 = 99995

Outcome	Win	Loss
Amount (x)	99995	-5
p	1/23500	23499/23500

Hence, expected value is -$0.74 showing I will make loss of $0.74 on an average if I play this game.

Answer is: -0.74

Please comment if any doubt. Thank you.