12.3 Odds

• Odds come in two forms, odds in favor of and odds against.
• When given, odds are always odds against unless stated otherwise.
• Odds against E = P(not E) / P(E)
• Odds in favor of E = P(E) / P(not E)
• Do Pgage 745 9, 13-16, 25, 26, 38

Expected Value

• Expected value is used to determine the results of an action over the long term.
• It predicts profit/loss each time an action occurs.
• E = ΣP_iA_i
  • Where P_i is the probability that event i occurs
  • And A_i is the amount (profit or loss ) when i occurs
  • Note: Each event must be disjoint
  • Note: Σ P_i = 1
• Fair Price = Expected Value + Price to Pay
• Fair Price is the amount to be paid that will result in an expected value of zero.
• Do page 756 number 12, 17, 20, 21, 27, 29, 45, 46