There are two different raffles you can enter. $\newline$ In raffle A, one ticket out of $50$ will win a $\$290$ prize. The other tickets will win nothing. Each ticket costs $\$9$ . $\newline$ Raffle B, which is at a carnival, has $500$ tickets. Each ticket costs $\$14$ . One ticket will win a $\$270$ prize, nine tickets will win a $\$240$ prize, eighteen tickets will win a $\$170$ prize, and the remaining tickets will win nothing. $\newline$ 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.

\newline

In raffle A, one ticket out of

50

will win a

\$290

prize. The other tickets will win nothing. Each ticket costs

\$9

\newline

Raffle B, which is at a carnival, has

500

tickets. Each ticket costs

\$14

. One ticket will win a

\$270

prize, nine tickets will win a

\$240

prize, eighteen tickets will win a

\$170

prize, and the remaining tickets will win nothing.

\newline

Which raffle is a better deal?

\newline

(A)Raffle A

\newline

(B)Raffle B

Calculate Expected Value Raffle A: Calculate the expected value for Raffle A. $\newline$ Expected value = $(\text{Probability of winning} \times \text{Prize value}) - (\text{Cost of ticket})$ $\newline$ Expected value for Raffle A = $\left(\frac{1}{50} \times \$(290)\right) - \$(9)$
Math Raffle A: Do the math for Raffle A. $\newline$ Expected value for Raffle A = $\left(\frac{\$290}{50}\right) - \$9$ $\newline$ Expected value for Raffle A = $\$5.80 - \$9$ $\newline$ Expected value for Raffle A = $-\$3.20$
Calculate Total Prize Money Raffle B: Calculate the total prize money for Raffle B. $\newline$ Total prize money = $1 * \$\(270$) + ($9$ * \$$240$) + ($18$ * \$$170$)(\newline\)Total prize money = \$$270$ + \$$2160$ + \$$3060$
Math Total Prize Money Raffle B: Do the math for the total prize money in Raffle B.$\newline$Total prize money = $\$270$ + $\$2160$ + $\$3060$$\newline$Total prize money = $\$5490$
Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.$\newline$Expected value = $(\text{Total prize money} / \text{Total number of tickets}) - (\text{Cost of ticket})$$\newline$Expected value for Raffle B = $(\$5490 / 500) - \$14$
Math Raffle B: Do the math for Raffle B.$\newline$Expected value for Raffle B = $\frac{ ext{ extdollar}5490}{500} - ext{ extdollar}14$$\newline$Expected value for Raffle B = $ ext{ extdollar}10.98 - ext{ extdollar}14$$\newline$Expected value for Raffle B = $- ext{ extdollar}3.02$
Compare Expected Values: Compare the expected values of both raffles to determine the better deal.$\newline$Raffle A has an expected value of $-\$3.20$.$\newline$Raffle B has an expected value of $-\$3.02$.$\newline$The raffle with the higher (less negative) expected value is the better deal.