2selz76t

2022-12-18

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$470 if your number is selected and nothing ($0) otherwise. (a) With a single$1 bet, what is the probability that you win $470? (b) Let X denote your winnings for a$1 bet, so x = $0 or x =$470. Construct the probability distribution for X. Use 3 decimal places.
X P(X)
$0$470
(c) The mean of the distribution equals $(d) Would this be considered a gain for you? No. For every$1 I pay, I will lose $0.53 on average. No. For every$1 I pay, I will lose $0.47 on average. Yes. For every$1 I pay, I will win $0.47 on average. (e) If you play "PICK 3" 100 times, how much should you expect to lose?$

drasticazuu

Expert

gurgtih91

Expert

d) No. Fow every $1 pay, i will lose$0.53 on average
e) $E\left(n\ast x\right)=n\ast E\left(x\right)=100\ast \left(-0.53\right)=-53$

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