Odds

• Gambling institutions commonly give probability in terms of odds.
• There are two forms of odds
  • Odds in favor of an event.
  • Odds against an event.
• Most casinos state the odds against unless otherwise noted.
• Odds on a horse race are different, other events.
• For an event E
  • The odds against E are P(not E) / P(E)
  • The odds in favor of E are P(E)/P(not E)
• Examples:
  • Lila is going to wear a blue dress and is trying to decide which pair of shoes she should wear. She has 12 pairs of shoes, 5 of which go well with the dress. If she selects a pair of shoes at random, find the
    • Odds in favor of the shoes going well with the dress
    • Odds against the shoes going well with the dress.
  • A die i s tossed
    • Find the odds against a two.
    • Find the odds in favor of an odd number
    • Find the odds in favor of a number greater than 4.
  • A single card is selected from a standard deck. Find the odds in favor and against
    • A king
    • A heart
    • The king of hearts
    • A face (picture) card
  • The odds in favor of Wendy winning a scholarship are 7:4.
    • What is the probability that she wins the scholarship.
    • What is the probability that she does not win the scholarship.