Question

One state lottery has 1,200 prizes of $1; 110 prizes of $10; 25 prizes of $70; 5 prizes of $290; 2 prizes of $1,210; and 1 prize of $2,500. Assume that 26,000 lottery tickets are issued and sold for $1.                

                            
What is the lottery's expected profit per ticket?

Answer 1

total amount for 26000 tickets = number of tickets*ticket price = 26000*$1 = $26000

Total amount given for prizes = 1200*$1 + 110*$10 + 25*$70 + 5*$290 + 2*$1210 + 1*$2500

this gives

Total amount given for prizes = 1200 + 1100 + 1750 + 1450+2420+ 2500 = $10420

So, Total profit = total amount for 26000 tickets - Total amount given for prizes = 26000-10420=15580

So, net profit is 15580 on 26000 tickets when sold for $1 per ticket

So, net profit per ticket = profit/(number of tickets) = 15580/26000 = $0.5992

Thus, Required profit per ticket is $0.5992.