The Nature of Mathematics, 12th Edition
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Section 13.2: Mathematical Expectation

13.2 Outline

A.  Expected value
      1. expected value (expectation)
      2. fair game
      3. mathematical expectation
B. 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                         

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