Section 12.3 Odds

What You Will Learn Odds Against Finding Probabilities from Odds

Odds The odds given at horse races, at craps, and at all gambling games in Las Vegas and other casinos throughout the world are always odds against unless they are otherwise specified.

Odds Against an Event The odds against an event is a ratio of the probability that the event will fail to occur (failure) to the probability that the event will occur (success). Thus, to find odds you must first know or determine the probability of success and the probability of failure.

Odds Against an Event The following formula may be used to determine the odds against an event.

Example 1: Rolling a 4 Determine the odds against rolling a 4 on one roll of a die. Solution odds against rolling a 4 The odds against rolling a 4 are 5:1.

Odds in Favor of an Event The following formula may be used to determine the odds in favor of an event.

Example 3: Smartphones The circle graph shows the U.S. market share for the operating systems used in Smartphones, as of December 2010.

Example 3: Smartphones If an individual who owns a smartphone is selected at random, use the graph to determine a) the odds against the individual owning a Google phone. Solution

Example 3: Smartphones Solution The odds against the individual owning a Google phone are 71:29.

Example 3: Smartphones If an individual who owns a smartphone is selected at random, use the graph to determine b) the odds in favor of the individual owning a Google phone. Solution The odds in favor of the individual owning a Google phone are 29:71.

Example 4: Determining Probabilities from Odds The odds against Robin Murphy being admitted to the college of her choice are 9:2. Determine the probability that (a) Robin is admitted and (b) Robin is not admitted.

Example 4: Determining Probabilities from Odds Solution The denominators must be 9 + 2 = 11. Odds against is a ratio of failure to success, the probabilities must be 9/11 (not admitted) and 2/11 (admitted).

Example 4: Determining Probabilities from Odds Solution a) The probability that Robin is admitted is 2/11. b) The probability that Robin is not admitted is 9/11.