A person is a running a lottery. There are a total of 1680 tickets numbered from
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Question
A person is a running a lottery. There are a total of 1680 tickets numbered from 1-1680. 177 people plat the lottery, the cost of playing is 0. If a single ticket wins, then the person wins the jackpot and earns 1000 dollars. If more than one person wins, they split the jackpot evenly. What is the expected payout for the person running the jackpot?
There are two cases here, either a person/more than one hits the jackpot and the person runnning the lottery has to payout $1000 or no one hits the jackpot in which this case the payout is $0. So I set it up like this E(payouy)=(1+2+...+177)(1/1680)(1000)+(1+2+...+177)(1-(1/1680))(0)=9376.785. Can anyone explain to me what I did wrong and how I should do it correctly?
Explanation / Answer
A person is a running a lottery. There are a total of 1680 tickets numbered from 1-1680. 177 people plat the lottery, the cost of playing is 0. If a single ticket wins, then the person wins the jackpot and earns 1000 dollars. If more than one person wins, they split the jackpot evenly. What is the expected payout for the person running the jackpot?
There are two cases here, either a person/more than one hits the jackpot and the person runnning the lottery has to payout $1000 or no one hits the jackpot in which this case the payout is $0. So I set it up like this E(payouy)=(1+2+...+177)(1/1680)(1000)+(1+2+...+177)(1-(1/1680))(0)=9376.785. Can anyone explain to me what I did wrong and how I should do it correctly?
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