There are two different raffles you can enter. Raffle A is for a $130 prize. Out of 200 tickets, each costing $1, one ticket will win the prize, and the other tickets will win nothing. In raffle B, one ticket out of 100 will win a $550 prize. The other tickets will win nothing. Each ticket costs $7. Which raffle is a better deal? Choices: (A)Raffle A (B)Raffle B

Calculate Expected Value: Calculate the expected value for Raffle A. E(A) = (Prize amount × Probability of winning) + (0 × Probability of losing) E(A) = ($130 × 1/200) + ($0 × 199/200) E(A) = $0.65 + $0 E(A) = $0.65Find Expected Profit: Subtract the cost of one ticket from the expected value of Raffle A to find the expected profit. Expected profit A = E(A) - Cost per ticket Expected profit A = $0.65 - $1 Expected profit A = -$0.35Calculate Expected Value: Calculate the expected value for Raffle B. E(B) = (Prize amount × Probability of winning) + (0 × Probability of losing) E(B) = ($550 × 1/100) + ($0 × 99/100) E(B) = $5.50 + $0 E(B) = $5.50Find Expected Profit: Subtract the cost of one ticket from the expected value of Raffle B to find the expected profit. Expected profit B = E(B) - Cost per ticket Expected profit B = $5.50 - $7 Expected profit B = -$1.50Compare Expected Profits: Compare the expected profits of Raffle A and Raffle B to determine which is the better deal. Since -$0.35 is greater than -$1.50, Raffle A is the better deal.

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There are two different raffles you can enter. $\newline$ Raffle A is for a $\$130$ prize. Out of $200$ tickets, each costing $\$1$ , one ticket will win the prize, and the other tickets will win nothing. $\newline$ In raffle B, one ticket out of $100$ will win a $\$550$ prize. The other tickets will win nothing. Each ticket costs $\$7$ . $\newline$ Which raffle is a better deal? $\newline$ Choices: $\newline$ (A)Raffle A $\newline$ (B)Raffle B

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Q. There are two different raffles you can enter.

\newline

Raffle A is for a

\$130

prize. Out of

200

tickets, each costing

\$1

, one ticket will win the prize, and the other tickets will win nothing.

\newline

In raffle B, one ticket out of

100

will win a

\$550

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

\$7

\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. $\newline$ E(A) = (\text{Prize amount} \times \text{Probability of winning}) + (0 \times \text{Probability of losing}) $\newline$ $E(A) = (\$(130) \times \frac{1}{200}) + (\$(0) \times \frac{199}{200})$ $\newline$ $E(A) = \$0.65 + \$0$ $\newline$ $E(A) = \$0.65$
Find Expected Profit: Subtract the cost of one ticket from the expected value of Raffle A to find the expected profit. $\newline$ Expected profit A = $E(A) - \text{Cost per ticket}$ $\newline$ Expected profit A = $(0.65) - (1)$ $\newline$ Expected profit A = $-(0.35)$
Calculate Expected Value: Calculate the expected value for Raffle B. $\newline$ $E(B) = (\text{Prize amount} \times \text{Probability of winning}) + (0 \times \text{Probability of losing})$ $\newline$ $E(B) = (\$(550) \times \frac{1}{100}) + (\$(0) \times \frac{99}{100})$ $\newline$ $E(B) = \$(5.50) + \$(0)$ $\newline$ $E(B) = \$(5.50)$
Find Expected Profit: Subtract the cost of one ticket from the expected value of Raffle B to find the expected profit. $\newline$ Expected profit B = $E(B) - \text{Cost per ticket}$ $\newline$ Expected profit B = $(\$5.50) - (\$7)$ $\newline$ Expected profit B = $-(\$1.50)$
Compare Expected Profits: Compare the expected profits of Raffle A and Raffle B to determine which is the better deal. $\newline$ Since $-\$0.35$ is greater than $-\$1.50$ , Raffle A is the better deal.