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There are two different raffles you can enter. $\newline$ Raffle A has $200$ tickets. Each ticket costs $\$17$ . One ticket will win a $\$190$ prize, and the remaining tickets will win nothing. $\newline$ Raffle B, which is for a fundraiser, has $250$ tickets. Each ticket costs $\$1$ . One ticket will win a $\$190$ prize, and the remaining tickets will win nothing. $\newline$ Which raffle is a better deal? $\newline$ Choices: $\newline$ (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.

\newline

Raffle A has

200

tickets. Each ticket costs

\$17

. One ticket will win a

\$190

prize, and the remaining tickets will win nothing.

\newline

Raffle B, which is for a fundraiser, has

250

tickets. Each ticket costs

\$1

. One ticket will win a

\$190

prize, and the remaining tickets will win nothing.

\newline

Which raffle is a better deal?

\newline

Choices:

\newline

(A)Raffle A

\newline

(B)Raffle B

Calculate Expected Value: Calculate the expected value for Raffle A. $\newline$ Expected value (EVA) = (Probability of winning $\times$ Prize amount) + (Probability of not winning $\times$ $0$ ) $\newline$ EVA = ( $\frac{1}{200}$ $\times$ $\$$ $190$ ) + ( $\frac{199}{200}$ $\times$ $\$$ $0$ ) $\newline$ EVA = $\$$ $0$ . $95$ + $\$$ $0$ $\newline$ EVA = $\$$ $0$ . $95$
Subtract Cost for Profit: Subtract the cost of one ticket from the expected value to find the expected profit for Raffle A. $\newline$ Expected profit (EPA) = Expected value - Cost per ticket $\newline$ $EPA = \$0.95 - \$17$ $\newline$ $EPA = -\$16.05$
Calculate Expected Value: Calculate the expected value for Raffle B. $\newline$ Expected value (EVB) = (Probability of winning $\times$ Prize amount) + (Probability of not winning $\times$ $0$ ) $\newline$ EVB = ( $\frac{1}{250}$ $\times$ $\$190$ ) + ( $\frac{249}{250}$ $\times$ $\$0$ ) $\newline$ EVB = $\$0.76$ + $\$0$ $\newline$ EVB = $\$0.76$
Subtract Cost for Profit: Subtract the cost of one ticket from the expected value to find the expected profit for Raffle B. $\newline$ Expected profit $EPB$ = Expected value - Cost per ticket $\newline$ $EPB = \$0.76 - \$1$ $\newline$ $EPB = -\$0.24$
Compare Expected Profits: Compare the expected profits of Raffle A and Raffle B to determine which is the better deal. $\newline$ Since $-\$16.05$ (Raffle A) is less than $-\$0.24$ (Raffle B), Raffle B is the better deal.

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