The state of Georgia has several statewide lottery options. One of the simpler ones is...

2selz76t

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? $

Answer & Explanation

drasticazuu

drasticazuu

Expert

2022-12-19Added 4 answers

a .   P ( $ ) 1 = 999 / 1000 P ( $ 470 ) 1 = 1 / 1000 b .   P d f = { ( 1 0.999 ) , ( 470 , 0.01 ) } c . E ( x ) = ( 1 0.999 ) + ( 470 0001 ) = $ 0.53
gurgtih91

gurgtih91

Expert

2022-12-20Added 1 answers

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

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