# World the bad part should be clear each win 10 does

• Notes
• 9
• 100% (1) 1 out of 1 people found this document helpful

This preview shows page 7 - 9 out of 9 pages.

world. The bad part should be clear. Each win (\$10) does not make up for each loss (\$11). In the long run, we would expect to lose money. We would not want to play this game. In this same example, if we only pay \$10.01 when we lose, the game is not nearly as unbalanced. It has a higher expectation. Example 3.12: In this game, when we win, we are paid \$10. When we lose, we pay \$10. Would we want to play this game?
8 If you have already answered (Yes or No), you have answered too soon. You don’t know what the probability of winning is. If your theoretical chance of winning is 50%, this is a fair game and playing is fine. If your theoretical chance of winning is 49%, the game is unfair, but not too unfair. If your theoretical chance of winning is 40%, the game is very unfair and playing would be very bad. Based on these examples, we see that your theoretical expectation is a combination of your probability of winning along with what you get paid when you win and what you pay when you lose. Definition 3.6: The mean of a discrete random variable X , is defined by the formula x Support xf x (provided the sum converges) ( ) . . .