674 CHAPTER 11 Probability Odds in Favor of an Event Although odds are generally given against an event, at times they may be given in favor of an event. The odds in favor of an event are expressed as a ratio of the probability that the event will occur to the probability that the event will fail to occur. b) From the graph, we see that 15%, or = , 15 100 3 20 of the students surveyed prefer Wrangler blue jeans. Therefore, the probability of a student preferring Wrangler blue jeans is . 3 20 The probability of a student not preferring Wrangler blue jeans is − = 1 . 3 20 17 20 = = = ⋅ = P P Odds against a student preferring Wrangler (student not preferring Wrangler) (student preferring Wrangler) 17 20 3 20 17 20 20 3 17 3 , or 17 : 3 Thus, the odds against a student preferring Wrangler blue jeans are 17 : 3. ■ Now try Exercise 41 Odds in Favor of an Event The following formula may be used to determine the odds in favor of an event. = = P P P P Odds in favor of event (event occurs) (event fails to occur) (success) (failure) If the odds against an event are a b : , the odds in favor of the event are b a : . Did You Know? Odds of Dying At some point, most people experience some fear associated with dying. This fear is normal and makes us cautious when going about our daily lives participating in various activities. However, the fear of dying due to a specific activity is often exaggerated compared to the actual odds in favor of dying due to that activity. Some common fears that may be exaggerated include fear of flying, fear of getting struck by lightning, and fear of getting attacked by a dog. Below is a table of the odds in favor of dying due to various causes for the year 2021. Note that the three fears mentioned above are quite low on the list. Cause of Death Odds in Favor of Dying Heart disease 1:5 Cancer 1: 6 COVID-19 1: 9 Opioid overdose 1: 57 Automobile accident 1: 92 Firearm assault 1: 207 Choking on food 1: 2659 Dog attack 1: 53,843 Airplane accident 1:188,363 Lightning strike 1: 218,105 Source: InjuryFacts.nsc.org Learning Catalytics Keyword: Angel-SOM-11.2 (See Preface for additional details.) Example 3 Selecting a Card One card is drawn from a standard 52-card deck. Determine a) the odds in favor of selecting a queen. b) the odds against selecting a queen. Solution a) There are 52 cards in a standard deck of cards, 4 of which are queens. Therefore, the probability of selecting a queen is , 4 52 or . 1 13 The probability the card selected is not a queen is − = 1 . 1 13 12 13 = = = ⋅ = P P Odds in favor of selecting a queen (selecting a queen) (not selecting a queen) 1 13 12 13 1 13 13 12 1 12 , or 1:12 Thus, the odds in favor of selecting a queen are 1 : 12. b) The odds against selecting a queen are 12 : 1. ■ Now try Exercise 19
RkJQdWJsaXNoZXIy NjM5ODQ=