The state of Georgia has several statewide lottery options. One of the simpler ones is a "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 $390 if your number is selected and nothing ($0) otherwise. (a) With a single $1 bet, what is the probability that you win $390?
(b) Let x denote your winnings for a $1 bet, so x = $0 or x = $390. Construct the probability distribution for X. Use 3 decimal places.
(c) The mean of the distribution equals X cents for the dollar paid to play.
(d) Would this be considered a gain for you?
No. For every $1 I pay, I will lose $0.39 on average.
No. For every $1 I pay, I will lose $ 0.61 on average.
Yes. For every $1 I pay, I will win $0.39 on average.
(e) If you play "PICK 3" 100 times, how much should you expect to lose?