4-1 Basic Concepts of Probability 157 A job recruiter claims that less than 50% of human resource professionals have turned down job applicants because of information found on social media. If the true rate is 50%, there is a 0.00000000978 probability of getting 148 or fewer human resource professionals who turn down job applicants because of information found on social media. If the true rate is 50%, is the result of 148 significantly low? What does that suggest about the claim that the rate is less than 50%? 39.Online Friends In a Pew Research Center survey of 1060 teens aged 13 to 17, it was found that 604 (or 57.0%) of those respondents have made new friends online. If the true rate is 50%, there is a probability of 0.00000306 of getting 604 or more respondents who have made new friends online. Is 604 significantly low, significantly high, or neither? What does the result suggest about the true rate being 50%? 40.Selfie Deaths Based on Priceonomics data describing 49 deaths while taking selfies, it was found that 37 of those deaths were males. Assuming that males and females are equally likely to have selfie deaths, there is a 0.000235 probability of getting 37 or more males. Is the result of 37 males significantly low, significantly high, or neither? Does the result suggest that male selfie deaths are more likely than female selfie deaths? Odds. In Exercises 41–44, answer the given questions that involve odds. 41. Florida Pick 3 In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499. a. Find the actual odds against winning. b. Find the payoff odds. c. Is there much of a difference between the actual odds against winning and the payoff odds? 42.Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number. a. What is your probability of winning? b. What are the actual odds against winning? c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $18 and win? d. How much profit would you make on the $18 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? (Recommendation: Don’t actually try to convince any casino of this; their sense of humor is remarkably absent when it comes to things of this sort.) 43. Kentucky Derby Odds When the horse Justify won the 144th Kentucky Derby, a $2 bet on a Justify win resulted in a winning ticket worth $7.80. a. How much net profit was made from a $2 win bet on Justify? b. What were the payoff odds against a Justify win? c. Based on preliminary wagering before the race, bettors collectively believed that Justify had a 0.1935 probability of winning. Assuming that 0.1935 was the true probability of a Justify victory, what were the actual odds against his winning? d. If the payoff odds were the actual odds found in part (c), what would be the worth of a $2 win ticket after the Justify win? 4-1 Beyond the Basics
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