Question

Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 6, nothing otherwise. What is your expected value?

Answer 1

1 down vote accepted The expected value is the sum of the probablity of each outcome multiplied by the "value" of each outcome. Its sort of like a special average. In your case each outcome has probability 16

. and you get 5 dollars when you roll 3 or 6 when you roll something else.

So the expected value is

06+06+56+06+06+56=106=53

.

This means loosely that if you played this game a lot you should expect to win on average about 1.66 dollars, while you payed 3 to play it. Clearly this is a great idea if you want to lose money.