Question

Question 5y>The student council is hosting a drawing to raise money for scholarships. They are selling tickets for$10 each and will sell 700 tickets.There is one $2,000 grand prize, two $500 second prizes, and eleven $40 third prizes. You justbought a ticket. Find the expected value for your profit. Round to the nearest cent.$Hint:HintVideo on Expected Value [+]Calculator

Answer 1

The expected value can be calculated using the formula

Probability of selecting tickets worth $2000 =

`\begin{gathered} (1)/(700) \\ \sin ce\text{ there is only one ticket which worth 2000 dollars } \end{gathered}`

Probability of selecting tickets worth $500 and

that of $40 are

`(2)/(700)\text{ and }(11)/(700)\text{ respectively }`

`\begin{gathered} (1)/(700) \\ \sin ce\text{ there is only one ticket which worth 2000 dollars } \end{gathered}`
`\begin{gathered} \Sigma_xP(x)=2000((1)/(700))+500((2)/(700))+40((11)/(700))-\cos t\text{ of a ticket } \\ \Sigma_xP(x)=2000((1)/(700))+500((2)/(700))+40((11)/(700))-10 \end{gathered}`

This becomes

`\begin{gathered} \Sigma_xP(x)=2000((1)/(700))+500((2)/(700))+40((11)/(700))-10 \\ \Sigma_xP(x)=(20)/(7)+(10)/(7)+(22)/(35)-10 \\ \Sigma_xP(x)=-(178)/(35) \\ \Sigma_xP(x)=-5.0857 \\ \Sigma_xP(x)=-5.09 \end{gathered}`

Hence the answer is $-5.09 to the nearest cent.