218 CHAPTER 5 Discrete Probability Distributions 5-1 Beyond the Basics 29.Expected Value for the Florida Pick 3 Lottery In the Florida Pick 3 lottery, you can bet $1 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $500. a. How many different selections are possible? b. What is the probability of winning? c. If you win, what is your net profit? d. Find the expected value for a $1 bet. e. If you bet $1 on the pass line in the casino dice game of craps, the expected value is -1.4¢. Which bet is better in the sense of producing a higher expected value: a $1 bet in the Florida Pick 3 lottery or a $1 bet on the pass line in craps? 30.Expected Value in North Carolina’s Pick 4 Game In North Carolina’s Pick 4 lottery game, you can pay $1 to select a four-digit number from 0000 through 9999. If you select the same sequence of four digits that are drawn, you win and collect $5000. a. How many different selections are possible? b. What is the probability of winning? c. If you win, what is your net profit? d. Find the expected value. e. If you bet $1 in North Carolina’s Pick 3 game, the expected value is -50.. Which bet is better in the sense of a producing a higher expected value: A $1 bet in the North Carolina Pick 4 game or a $1 bet in the North Carolina Pick 3 game? 31.Expected Value in Roulette When playing roulette at the Venetian casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 27 or to bet $5 that the outcome is any one of these five possibilities: 0, 00, 1, 2, 3. The expected value of the $5 bet for a single number is -26.. For the $5 bet that the outcome is 0, 00, 1, 2, or 3, there is a probability of 5>38 of making a net profit of $30 and a 33>38 probability of losing $5. a. Find the expected value for the $5 bet that the outcome is 0, 00, 1, 2, or 3. b. Which bet is better: a $5 bet on the number 27 or a $5 bet that the outcome is any one of the numbers 0, 00, 1, 2, or 3? Why? 32.Life Insurance There is a 0.99963 probability that a randomly selected 20-year-old female lives through the year (based on data from the U.S. Department of Health and Human Services). An insurance company wants to offer her a one-year policy with a death benefit of $1,000,000. How much should the company charge for this policy if it wants an expected return of $400 from all similar policies? Key Concept Section 5-1 introduced the important concept of a discrete probability distribution. Among the various discrete probability distributions that exist, the focus of this section is the binomial probability distribution. Part 1 of this section introduces the binomial probability distribution along with methods for finding probabilities. Part 2 presents easy methods for finding the mean and standard deviation of a binomial distribution. As in other sections, we stress the importance of interpreting probability values to determine whether events are significantly low or significantly high. 5-2 Binomial Probability Distributions
RkJQdWJsaXNoZXIy NjM5ODQ=