Concept explainers
Straight or boxed? Consider a Pick-3 lottery such as the one described in Exercise 6.7. Suppose your birthday is May 14, and like many people, you decide to bet $1 on your birthday number (i.e., 514) on your birthday. There are two options to play, straight or boxed. If you choose to play straight, you win $500 if and only if the number chosen is 514. If you choose to play boxed, you win $80 if the number chosen contains the digits 5, 1, and 4 in any order. Which option would you prefer to play and why?
6.7 Playing the lottery The state of Ohio has several statewide lottery options. One is the Pick 3 game in which you pick one of the 1000 three-digit numbers between 000 and 999. The lottery selects a three-digit number at random. With a bet of $1, you win $500 if your number is selected and nothing ($0) otherwise. (Many states have a very similar type of lottery.) (Source: Background information from www.ohiolottery.com.)
- a. With a single $1 bet, what is the probability that you win $500?
- b. Let X denote your winnings for a $1 bet, so x = $0 or x = $500. Construct the probability distribution for X.
- c. Show that the
mean of the distribution equals 0.50, corresponding to an expected return of 50 cents for the dollar paid to play. Interpret the mean. - d. In Ohio’s Pick 4 lottery, you pick one of the 10,000 four-digit numbers between 0000 and 9999 and (with a $1 bet) win $5000 if you get it correct. In terms of your expected winnings, with which game are you better off—playing Pick 4, or playing Pick 3? Justify your answer.
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Statistics: The Art and Science of Learning from Data (4th Edition)
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