SOLUTION: One state lottery has 1,100 prizes of $1, 105 prizes of $10, 25 prizes of $60, 5 prizes of $290, 2 prizes of $1,180, and 1 prize of $2,600. Assume that 26,000 lottery tickets are i

Question 1068562: One state lottery has 1,100 prizes of $1, 105 prizes of $10, 25 prizes of $60, 5 prizes of $290, 2 prizes of $1,180, and 1 prize of $2,600. Assume that 26,000 lottery tickets are issued and sold for $1.
What is the lottery's expected profit per ticket? Four Decimal Points
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The lottery makes $26000 on sales
It pays out:
$1*1100=$1100
$10*105=$1050
$60*25=$1500
$290*5=$1450
$1180*2=$2360
$2600*1=$2600
Total is $10,060
The fraction paid out is 10,060/26,000=0.3869
so their expected profit per $1 is $0.6131

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One state lottery has 1,100 prizes of $1 , 1,105 prizes of $10, 25 prizes of $60, 5 prizes of $290, 2 prizes of $1,180, and 1 prize of $2,600. Assume that 26,000 lottery tickets are issued and sold for $1.
What is the lottery's expected profit per ticket? Four Decimal Points
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Random "winnings":: 1; 10 ; 60 ; 290 ; 1180 ; 2600 ; -1
Probs : 1100/26000.1105/26000.25/26000.5/26000.2/26000.1/26000. 24900/26000
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E(x) = [1100*1 + 1105*10 + 25*60 + 5*290 + 2*1180 + 1*2600 +(24900*(-1))]/26000
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= [1100 + 11050 + 1500 + 1450 + 2360 + 2600 - 24900]/26000
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= -4840/26000
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= -18.6 cents (Each ticket purchaser can expect to lose 18.6
cents for each ticket bought)
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Ans:: Expected lottery profit is 18.6 cents per ticket sold.
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Cheers,
Stan H.
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Answer::
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