# Question: The state of Ohio has several statewide lottery options One

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 in which you win $500 for a correct choice of a three-digit number? Justify your answer.

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 in which you win $500 for a correct choice of a three-digit number? Justify your answer.

## Answer to relevant Questions

The wingspans of recently cloned monarch butterflies follow a normal distribution with mean 9 inches and standard deviation 0.75 inches. What proportion of the butterflies has a wingspan a. Less than 8 inches? b. Wider than ...In a study carried out at the Infant Cognition Center at Yale University, researchers showed 16 infants two videos: one featured a character that could be perceived as helpful, and the other featured a character that could ...A salesperson uses random digit dialing to call people and try to interest them in applying for a charge card for a large department store chain. From past experience, she is successful on 2% of her calls. In a typical ...Most discrete random variables can take on a finite number of values. Let X = the number of rolls of two dice necessary until doubles (the same number on each die) first appears. The possible values for this discrete random ...A roulette wheel in Las Vegas has 38 slots. If you bet a dollar on a particular number, you’ll win $35 if the ball ends up in that slot and $0 otherwise. Roulette wheels are calibrated so that each outcome is equally ...Post your question