2selz76t

Answered

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? $

(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? $

Answer & Explanation

drasticazuu

Expert

2022-12-19Added 4 answers

$a.\text{}P(-\$)1=999/1000\phantom{\rule{0ex}{0ex}}P(\$470)1=1/1000\phantom{\rule{0ex}{0ex}}b.\text{}{P}_{df}=\{(-1\ast 0.999),(470,0.01)\}\phantom{\rule{0ex}{0ex}}c.E(x)=(-1\ast 0.999)+(470\ast 0001)=-\$0.53$

gurgtih91

Expert

2022-12-20Added 1 answers

d) No. Fow every $1 pay, i will lose $0.53 on average

e) $E(n\ast x)=n\ast E(x)=100\ast (-0.53)=-\$53$

e) $E(n\ast x)=n\ast E(x)=100\ast (-0.53)=-\$53$

Most Popular Questions