There are two different raffles you can enter. Raffle A, which is for a fundraiser, has $125$ tickets. Each ticket costs $\$15$ . One ticket will win a $\$560$ prize, and the remaining tickets will win nothing. In raffle B, one ticket will win a $\$440$ prize, one ticket will win a $\$390$ prize, one ticket will win a $\$380$ prize, one ticket will win a $\$90$ prize, and the rest will win nothing. There are $125$ in the raffle, each costing $\$20$ . Which raffle is a better deal? $\newline$ (A)Raffle A $\newline$ (B)Raffle B

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Choose the better bet

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Q. There are two different raffles you can enter. Raffle A, which is for a fundraiser, has

125

tickets. Each ticket costs

\$15

. One ticket will win a

\$560

prize, and the remaining tickets will win nothing. In raffle B, one ticket will win a

\$440

prize, one ticket will win a

\$390

prize, one ticket will win a

\$380

prize, one ticket will win a

\$90

prize, and the rest will win nothing. There are

125

in the raffle, each costing

\$20

. Which raffle is a better deal?

\newline

(A)Raffle A

\newline

(B)Raffle B

Calculate Total Cost Raffle A: Calculate the total cost for all tickets in Raffle A. $\newline$ Total cost for Raffle A = Number of tickets * Cost per ticket = $125$ tickets * $\$15$ /ticket
Calculate Expected Value Raffle A: Total cost for Raffle A = $125$ \times \$($15$) = \$($1875$)
Calculate Total Cost Raffle B: Calculate the expected value for a single ticket in Raffle A.$\newline$Expected value for Raffle A = $(\text{Prize value} - \text{Total cost}) / \text{Number of tickets}$ = $(\$560 - \$1875) / 125$
Calculate Total Prize Value Raffle B: Expected value for Raffle A = $(\$560 - \$1875) / 125 = -\$10.52$ per ticket
Calculate Expected Value Raffle B: Calculate the total cost for all tickets in Raffle B.$\newline$Total cost for Raffle B = Number of tickets * Cost per ticket = $125$ tickets * $\$20$/ticket
Compare Expected Values: Total cost for Raffle B = $125$ \times $\(20$) = \$($2500$)
Compare Expected Values: Total cost for Raffle B = $125$ \times $\(20$) = \$($2500$)Calculate the total prize value for Raffle B.$\newline$Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$)
Compare Expected Values: Total cost for Raffle B = $125$ \times $\(20$) = \$($2500$)Calculate the total prize value for Raffle B.$\newline$Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$)Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$) = \$($1300$)
Compare Expected Values: Total cost for Raffle B = $125$ \times $\(20$) = \$($2500$)Calculate the total prize value for Raffle B.$\newline$Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$)Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$) = \$($1300$)Calculate the expected value for a single ticket in Raffle B.$\newline$Expected value for Raffle B = (Total prize value - Total cost) / Number of tickets = (\$($1300$) - \$($2500$)) / $125$
Compare Expected Values: Total cost for Raffle B = $125$ * $\(20$) = \$($2500$)Calculate the total prize value for Raffle B.$\newline$Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$)Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$) = \$($1300$)Calculate the expected value for a single ticket in Raffle B.$\newline$Expected value for Raffle B = (Total prize value - Total cost) / Number of tickets = (\$($1300$) - \$($2500$)) / $125$Expected value for Raffle B = (\$($1300$) - \$($2500$)) / $125$ = -\$($9$.$6$) per ticket
Compare Expected Values: Total cost for Raffle B = $125$ \times $\(20$) = \$($2500$)Calculate the total prize value for Raffle B.$\newline$Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$)Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$) = \$($1300$)Calculate the expected value for a single ticket in Raffle B.$\newline$Expected value for Raffle B = (Total prize value - Total cost) / Number of tickets = (\$($1300$) - \$($2500$)) / $125$Expected value for Raffle B = (\$($1300$) - \$($2500$)) / $125$ = -\$($9$.$6$) per ticketCompare the expected values of both raffles to determine which is a better deal.$\newline$Raffle A has an expected value of -\$($10$.$52$) per ticket, and Raffle B has an expected value of -\$($9$.$6$) per ticket.
Compare Expected Values: Total cost for Raffle B = $125$ \times \$($20$) = \$($2500$)Calculate the total prize value for Raffle B.$\newline$Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$)Total prize value for Raffle B = \$($440$) + \$($390$) + \$($380$) + \$($90$) = \$($1300$)Calculate the expected value for a single ticket in Raffle B.$\newline$Expected value for Raffle B = (Total prize value - Total cost) / Number of tickets = (\$($1300$) - \$($2500$)) / $125$Expected value for Raffle B = (\$($1300$) - \$($2500$)) / $125$ = -\$($9$.$6$) per ticketCompare the expected values of both raffles to determine which is a better deal.$\newline$Raffle A has an expected value of -\$($10$.$52$) per ticket, and Raffle B has an expected value of -\$($9$.$6$) per ticket.Since Raffle B has a higher expected value (less negative), it is the better deal.