Odds

• Odds are another way to express probability.
• The Odds against an event E = P(not E)/P(E)
• The Odds in favor of an event E = P(E)/P(not E)
• Odds at most gambling establishments are odds against unless otherwise noted.
• If the odds of an event E occurring are a/b, P(E) = a/(a+b)
• Do exercises P 745 9, 13-16, 17-20,

Expected Value

• Expected value is a tool to determine what will happen in the long run in a game that involves profit or loss.
• E = P₁×A₁ + P₂×A₂+ ... + P_n×A_n
• The individual events should be disjoint.
• The individual events should cover the entire event space.
• The Fair Price for a game is expected value + price to play
• Do Page 756 number 11, 12, 17
• A card is drawn from a standard 52 card deck and you win if a heart is drawn. If you pay $15 to play the game, and are paid $30 if you win, what is the expected value of the game.
• Do problem 26