This document defines key terms related to odds and probability, including the odds in favor of and against an event, and how to calculate probabilities from odds ratios. It provides examples of calculating odds of rolling certain numbers on a die or drawing particular cards. The document also discusses what constitutes a fair game based on odds and how house odds relate to payouts on bets.

1. ODDSBy Christy Swindler

2. Important Definitions/Symbols of ODDSP(E) is the probability of an event E occurringP(not E) is the probability of an event E Not occurring

3. Probability to ODDS1. The odds in favor of E = P(E)/P(not E)2. The odds against E = P(not E)/P(E) The odds against E can also be found by reversing the ratio representing the odds in favor of E.

4. EXAMPLEIN FAVORAGAINSTRoll a 6-sided die. Find the odds in favor of rolling a 2. P(E)=1/6, P(not E)=5/6 1/6 divided by 5/6=1/5The odds in favor of rolling a 2 are 1 to 5.Roll a 6-sided die. Find the odds against rolling a 2. By reversing the above ratio, the odds against rolling a 2 is 5 to 1.

5. Card ExampleYou are dealt a card from a 52-card deck. Find the odds in favor and against getting a red queen.P(red queen) = 2/52

6. P(not red queen) = 1-2/52 = 50/52

7. Odds in favor of red queen= (2/52)divided by (50/52)=2/50=1/25

8. Odds against a red queen= 25/1.FAIR GAME???If the odds in favor of an event E are a to b,the game is fair if a bet of $a is lost if event E does NOT occur.

9. the game is fair if a bet of $b is won (plus the original investment) if event E DOES occur.House Odds Tells the gambler what the payoff is on the betThe odds given are usually odds against