Section 13.2: Mathematical Expectation

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13.2 Outline

  1. Expected value
    1. expected value (expectation)
    2. fair game
    3. mathematical expectation
  2. Expectation with a cost of playing
    1. definition
    2. 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