Question

A lottery ticket costs $5. You pick 3 two-digit numbers (anything from 00 to 99) in order.

If you match the first number only, you win $200.
If you match the first two numbers and not the third, you win $5000.
If you match all three numbers, you win $100,000.
In two or more complete sentences, explain whether or not the game is fair. In your explanation, include all necessary calculations.

Answer 1

this one's a bit difficult to explain but I'll try

for a game to be fair, the "expected value" must be equal to the cost of playing the game. the expected value can be calculated by finding the probability of winning each amount of money, times the amount of money won, added together like this:

expected value = (probability of winning $200)*200 + (probability of winning $5000)*5000 + (probability of winning 100,000)*100000 - (probability of losing)(5)

in this case, if the expected value is 5, then the game is fair. Otherwise, the game is unfair.