There are two different raffles you can enter. $\newline$ Raffle A has $250$ tickets. Each ticket costs $\$20$ . One ticket will win a $\$610$ prize, and the remaining tickets will win nothing. $\newline$ In raffle B, one ticket out of $200$ will win a $\$630$ prize, and one ticket will win a $\$50$ prize. The remaining tickets will win nothing. Each ticket costs $\$17$ . $\newline$ 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

Raffle A has

250

tickets. Each ticket costs

\$20

. One ticket will win a

\$610

prize, and the remaining tickets will win nothing.

\newline

In raffle B, one ticket out of

200

will win a

\$630

prize, and one ticket will win a

\$50

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

\$17

\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 = $(\text{Probability of winning} \times \text{Prize value}) - (\text{Ticket cost})$ $\newline$ For Raffle A, the probability of winning is $\frac{1}{250}$ , and the prize is $\$610$ . $\newline$ Expected value for Raffle A = $\left(\frac{1}{250} \times \$610\right) - \$20$
Perform Calculation Raffle A: Perform the calculation for Raffle A. $\newline$ Expected value for Raffle A = \frac{$1$}{$250$} * (\$)$610) - (\$)\(20$(\newline\)Expected value for Raffle A = (\$)$2$.$44$ - (\$)$20$$\newline$Expected value for Raffle A = -(\$)$17$.$56$
Calculate Expected Value Raffle B: Calculate the expected value for Raffle B. There are two prizes, so we need to calculate the expected value for each prize and then add them together. For the $\$630$ prize, the probability of winning is $\frac{1}{200}$. For the $\$50$ prize, the probability of winning is also $\frac{1}{200}$. Expected value for Raffle B = $\left(\frac{1}{200} \times \$630 + \frac{1}{200} \times \$50\right) - \$17$
Perform Calculation Raffle B: Perform the calculation for Raffle B.$\newline$Expected value for Raffle B = $\frac{\(1$}{$200$} * (\$)$630$ + \frac{$1$}{$200$} * (\$)$50$) - (\$)$17$(\newline\)Expected value for Raffle B = $(\$)\(3$.$15$ + (\$)$0$.$25$) - (\$)$17$(\newline\)Expected value for Raffle B = (\$)$3$.$40$ - (\$)$17$(\newline\)Expected value for Raffle B = -(\$)$13$.$60$
Compare Expected Values: Compare the expected values of Raffle A and Raffle B to determine the better deal.$\newline$Raffle A has an expected value of $-\$17.56$.$\newline$Raffle B has an expected value of $-\$13.60$.$\newline$Since the expected value is less negative for Raffle B, it is the better deal.