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There are two different raffles you can enter. $\newline$ Out of $200$ tickets in raffle A, each costing $\$20$ , one ticket will win a $\$880$ prize. The other tickets will win nothing. $\newline$ Raffle B has $250$ tickets, and each costs $\$10$ . One ticket will win a $\$510$ prize, one ticket will win a $\$450$ prize, one ticket will win a $\$250$ prize, and one ticket will win a $\$30$ prize. The rest 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

Full solution

Q. There are two different raffles you can enter.

\newline

Out of

200

tickets in raffle A, each costing

\$20

, one ticket will win a

\$880

prize. The other tickets will win nothing.

\newline

Raffle B has

250

tickets, and each costs

\$10

. One ticket will win a

\$510

prize, one ticket will win a

\$450

prize, one ticket will win a

\$250

prize, and one ticket will win a

\$30

prize. The rest 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 = $(\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})$ $\newline$ Expected value for Raffle A = $\left(\frac{1}{200} \times \$(880)\right) - \left(\frac{199}{200} \times \$(20)\right)$
Perform Calculations Raffle A: Perform the calculations for Raffle A. $\newline$ Expected value for Raffle A = ( $4.40) - ($ $19$ . $90$ ) $\newline$ Expected value for Raffle A = -$\(15\).\(50\)
Calculate Expected Value Raffle B: Calculate the expected value for Raffle B.\(\newline\)Expected value = \((\text{Probability of winning the }\$510 \text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$450 \text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$250 \text{ prize} \times \text{Prize value}) + (\text{Probability of winning the }\$30 \text{ prize} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})\)\(\newline\)Expected value for Raffle B = \((\frac{1}{250} \times \$510) + (\frac{1}{250} \times \$450) + (\frac{1}{250} \times \$250) + (\frac{1}{250} \times \$30) - (\frac{246}{250} \times \$10)\)
Perform Calculations Raffle B: Perform the calculations for Raffle B.\(\newline\)Expected value for Raffle B = \((\$2.04) + (\$1.80) + (\$1.00) + (\$0.12) - (\$9.84)\)\(\newline\)Expected value for Raffle B = \(\$5.96 - \$9.84\)\(\newline\)Expected value for Raffle B = \(-\$3.88\)

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