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There are two different raffles you can enter. $\newline$ Out of $250$ tickets in raffle A, each costing $\$7$ , one ticket will win a $\$460$ prize. The remaining tickets will win nothing. $\newline$ Raffle B has $50$ tickets, and each costs $\$14$ . One ticket will win a $\$790$ prize, one ticket will win a $\$760$ prize, one ticket will win a $\$710$ prize, and one ticket will win a $\$20$ prize. 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

Full solution

Q. There are two different raffles you can enter.

\newline

Out of

250

tickets in raffle A, each costing

\$7

, one ticket will win a

\$460

prize. The remaining tickets will win nothing.

\newline

Raffle B has

50

tickets, and each costs

\$14

. One ticket will win a

\$790

prize, one ticket will win a

\$760

prize, one ticket will win a

\$710

prize, and one ticket will win a

\$20

prize. 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 = $(\text{Probability of winning} \times \text{Prize value}) - (\text{Probability of losing} \times \text{Cost per ticket})$ $\newline$ Expected value for Raffle A = $\left(\frac{1}{250} \times \$(460)\right) - \left(\frac{249}{250} \times \$(7)\right)$
Perform Calculations Raffle A: Perform the calculations for Raffle A. $\newline$ Expected value for Raffle A = $(\$1.84) - (\$6.972)$ $\newline$ Expected value for Raffle A = $-\$5.132$
Calculate Expected Value Raffle B: Calculate the expected value for Raffle B. $\newline$ Expected value for Raffle B = (Probability of winning the $\$$ $790$ prize $*$ Prize value) + (Probability of winning the $\$$ $760$ prize $*$ Prize value) + (Probability of winning the $\$$ $710$ prize $*$ Prize value) + (Probability of winning the $\$$ $20$ prize $*$ Prize value) - (Probability of losing $*$ Cost per ticket) $\newline$ Expected value for Raffle B = (\frac{\(1\)}{\(50\)} \(* \$\(790\)) + (\frac{\(1\)}{\(50\)} \(*\) \$\(760\)) + (\frac{\(1\)}{\(50\)} \(*\) \$\(710\)) + (\frac{\(1\)}{\(50\)} \(*\) \$\(20\)) - (\frac{\(46\)}{\(50\)} \(*\) \$\(14\))\)
Perform Calculations Raffle B: Perform the calculations for Raffle B.\(\newline\)Expected value for Raffle B = \((\$15.8 + \$15.2 + \$14.2 + \$0.4) - (\$13.16)\)\(\newline\)Expected value for Raffle B = \(\$45.6 - \$13.16\)\(\newline\)Expected value for Raffle B = \(\$32.44\)

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