Statistics problem...?

The state of Ohio has several statewide lottery options (www.ohiolottery.com). One of the simpler ones is a “Pick 3” game in which you pick one of the 1000 3-digit numbers between 000 and 999. The lottery selects a 3-digit number at random. With a bet of $1, you win $500 if your number is selected and nothing ($0) otherwise. The Florida lottery has the same game (called CASH 3, with the STRAIGHT play option) and the same winnings structure.





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.

Statistics problem...?
a.


P(win 500) = 1/1000 = 0.001





b.


P(x=$0) = 999/1000 = 0.999


P(x=$500) = 1/1000 = 0.001





c.


E(X) = (0)(0.999) + (500)(0.001) = 0.50