Question

We are going to play a game of chance. We will roll a die (half of a pair of dice) and if it comes up with one or two spots showing, you win and I will pay you $1.50. If it comes up with three, four, five, or six spots showing, you lose and you will pay me $1.20. So, the probability that you will win is 1/3 and the probability you will lose is 2/3. Your financial benefit will be either +$1.50 or -$1.20.

What is the expected value of this game for you? (show calculations)

Would you want to play this game? Why?

If we played the game 100 times, about how much would you expect to win or lose in total? Note: The “expected value” of a random process is the long-term average winning/loss per play of the game if you were to play many times.

Answer 1

Suppose, random variable X denotes amount won by me.

So, probability mass function is given by

Expected value of the game is given by

So, expected value of this game for me = $ -0.30

As expected value for me is negative indicating loss in the game, I shall not want to play this game.

If we played the game 100 times, expected amount to lose in total = $ (100*0.30) = $ 30