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There are two different raffles you can enter. Raffle A, which is at a carnival, has $125$ tickets. Each ticket costs $\$4$ . One ticket will win a $\$280$ prize, and the remaining tickets will win nothing. Out of $50$ tickets in raffle B, each costing $\$15$ , one ticket will win a $\$480$ prize, and one ticket will win a $\$210$ prize. The remaining tickets will win nothing. Which raffle is a better deal? $\newline$ (A)Raffle A $\newline$ (B)Raffle B

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Choose the better bet

Full solution

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

125

tickets. Each ticket costs

\$4

. One ticket will win a

\$280

prize, and the remaining tickets will win nothing. Out of

50

tickets in raffle B, each costing

\$15

, one ticket will win a

\$480

prize, and one ticket will win a

\$210

prize. The remaining tickets will win nothing. Which raffle is a better deal?

\newline

(A)Raffle A

\newline

(B)Raffle B

Calculate Total Cost Raffle A: Calculate the total cost of all tickets for Raffle A. $\newline$ Total cost for Raffle A = Number of tickets * Cost per ticket $\newline$ Total cost for Raffle A = \(125\) * \(\$4\)\(\newline\)Total cost for Raffle A = \(\$500\)
Calculate Expected Value Raffle A: Calculate the expected value of a ticket in Raffle A.\(\newline\)Expected value for Raffle A = \((\text{Prize value} - \text{Total cost}) / \text{Number of tickets}\)\(\newline\)Expected value for Raffle A = \((\$280 - \$500) / 125\)\(\newline\)Expected value for Raffle A = \(-\$1.76\)
Calculate Total Cost Raffle B: Calculate the total cost of all tickets for Raffle B.\(\newline\)Total cost for Raffle B = Number of tickets * Cost per ticket\(\newline\)Total cost for Raffle B = $50$ * $\$15$ $\newline$ Total cost for Raffle B = $\$750$
Calculate Expected Value Raffle B: Calculate the expected value of a ticket in Raffle B. $\newline$ Expected value for Raffle B = $(\text{Total prize value} - \text{Total cost}) / \text{Number of tickets}$ $\newline$ Expected value for Raffle B = $(\$(480) + \$(210) - \$(750)) / 50$ $\newline$ Expected value for Raffle B = $-\$(1.20)$
Compare Expected Values: Compare the expected values of both raffles to determine the better deal. Raffle A has an expected value of $-\$1.76$ per ticket, and Raffle B has an expected value of $-\$1.20$ per ticket. Since the expected value is less negative for Raffle B, it is the better deal.

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