Question

One state lottery has 1,100 prizes of $1; 105 prizes of $10; 25 prizes $50; 5 prizes of $280; 2 prizes of $1,190; and 1 prize of $2,300. Assume that 36,000 lottery tickets are issued and sold for $1.

1. What is the lottery’s expected profit per ticket?

2. What is the lottery’s standard deviation of profit per ticket?

Answer 1

Here first let find the distribution of X which is the profit per ticket.

The possible value of X's are $0, $9, $49, $179, $1189, $2299 and -$1.

The corresponding probabilities and necessary calculations,

Profit(Xi)	Freq	Probability(Pi)	XiPi	Xi2Pi
0	1100	0.030555556	0	0
9	105	0.002916667	0.02625	0.23625
49	25	0.000694444	0.034028	1.667361
179	5	0.000138889	0.024861	4.450139
1189	2	5.55556E-05	0.066056	78.54006
2299	1	2.77778E-05	0.063861	146.8167
-1	34762	0.965611111	-0.96561	0.965611
Total	36000	1	-0.75056	232.6761

1) Mean = -0.75056

2) SD = [ 232.6761 - (-0.75056)² ]^1/2 = 15.23525.