13.2 Outline
- Expected value
- expected value (expectation)
- fair game
- mathematical expectation
- Expectation with a cost of playing
- definition
- roulette wheel and board
13.2 Essential Ideas
If an event E has several possible outcomes with probabilities p1, p2, p3, …, and if for each of these outcomes the amount that can be won is a1, a2, a3, … , respectively, then the mathematical expectation (or expected value) of E is
EXPECTATION = a1p1 + a2p2 + a3p3 + …
If there is a cost of playing a game, the cost of playing must be subtracted from the expectation.
EXPECTATION = AMT. TO WIN(PROB. OF WINNING) – COST OF PLAYING