1. Gamblers usually give odds against an event happening. For instance, if a bookie gives the odds 4 to 1 that the Yankees will win the next World Series, he is stating that the probability that the Yankees will win is 1/5, or .2. Also, if a bettor bets $1 that the Yankees will win and the Yankees do win, then the bettor will receive $5 (his original bet plus a profit of $4). The following are typical odds set by a bookie for the eventual winner in a fictitious four-team league: Sparks (5 to 3), Meteors (3 to 1), Asteroids (3 to 2), Suns (4 to 1).
(a) Convert the odds to probabilities of winning for each team.
(b) Add the four probabilities.
(c) Explain why the answer to (b) makes sense.
2. The probability that there will be a major earthquake in the San Francisco area during the next 30 years is .63. What are the corresponding odds?