Question

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?

Answer 1

1/ 1000 ;

X : _____ 0 ___________ 390

P(x) : ___ 999/1000 ___ 1/ 1000 ;

0.39 ;

D ;

-$61

Explanation:

1.)

Probability of winning with a single bet:

Winning numbers in lottery = 1

Lottery size = 1000

P(winning per bet) = 1/ 1000

2.)

X : _____ 0 ___________ 390

P(x) : ___ 999/1000 ___ 1/ 1000

3.)

Σx*p(x)

(0 * 999/1000) + (390 * 1/1000)

0 + 390 / 1000

= 0.39

4)

Expected winning :

Loss = - 1 * 999/1000 ; win = 390 * 1/1000

- 0.999 + 0.39 = - 0.609 = - $0.61

Hence, on average, for every $1 bet, I lose $0.61 on average

E.)

Expected winning for playing 100 times ;

Loss per play:

Expected winning * 100

-$0.61 * 100 = -$61

Loss of - $61 on average