Section 12 3 Odds Copyright 2013 2010 2007

What You Will Learn Odds Against Finding Probabilities from Odds 12. 3 -2 Copyright

Odds The odds given at horse races, at craps, and at all gambling games

Odds Against an Event The odds against an event is a ratio of the

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

Example 1: Rolling a 4 Determine the odds against rolling a 4 on one

Odds in Favor of an Event The following formula may be used to determine

Example 3: Smartphones The circle graph shows the U. S. market share for the

Example 3: Smartphones If an individual who owns a smartphone is selected at random,

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

Example 4: Determining Probabilities from Odds The odds against Robin Murphy being admitted to

Example 4: Determining Probabilities from Odds Solution The denominators must be 9 + 2

Example 4: Determining Probabilities from Odds Solution a) The probability that Robin is admitted

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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. 12. 3 -3 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 12. 3 -4 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 12. 3 -6 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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 12. 3 -9 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 12. 311 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 12. 312 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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). 12. 313 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 12. 314 Copyright 2013, 2010, 2007, Pearson, Education, Inc.