Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

There are two different raffles you can enter.\newlineIn raffle A, one ticket out of 5050 will win a $290\$290 prize. The other tickets will win nothing. Each ticket costs $9\$9.\newlineRaffle B, which is at a carnival, has 500500 tickets. Each ticket costs $14\$14. One ticket will win a $270\$270 prize, nine tickets will win a $240\$240 prize, eighteen tickets will win a $170\$170 prize, and the remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Choose the better betright chevron icon

Full solution

Q. There are two different raffles you can enter.\newlineIn raffle A, one ticket out of 5050 will win a $290\$290 prize. The other tickets will win nothing. Each ticket costs $9\$9.\newlineRaffle B, which is at a carnival, has 500500 tickets. Each ticket costs $14\$14. One ticket will win a $270\$270 prize, nine tickets will win a $240\$240 prize, eighteen tickets will win a $170\$170 prize, and the remaining tickets will win nothing.\newlineWhich raffle is a better deal?\newline(A)Raffle A\newline(B)Raffle B
  1. Calculate Expected Value Raffle A: Calculate the expected value for Raffle A.\newlineExpected value = (\text{Probability of winning} \times \text{Prize value}) - (\text{Cost of ticket})\newlineExpected value for Raffle A = (150×$(290))−$(9)\left(\frac{1}{50} \times \$(290)\right) - \$(9)
  2. Math Raffle A: Do the math for Raffle A.\newlineExpected value for Raffle A = ($29050)−$9\left(\frac{\$290}{50}\right) - \$9\newlineExpected value for Raffle A = $5.80−$9\$5.80 - \$9\newlineExpected value for Raffle A = −$3.20-\$3.20
  3. Calculate Total Prize Money Raffle B: Calculate the total prize money for Raffle B.\newlineTotal prize money = \(1 * \$\(270\)) + (\(9\) * \$\(240\)) + (\(18\) * \$\(170\))(\newline\)Total prize money = \$\(270\) + \$\(2160\) + \$\(3060\)
  4. 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 = \(\$5490\)
  5. 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 = \((\$5490 / 500) - \$14\)
  6. 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 = \(- ext{ extdollar}3.02\)
  7. 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.

More problems from Choose the better bet

Question
A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well. \newlineIf the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?\newlineWrite your answer as a decimal rounded to the nearest thousandth.
Get tutor helpright-arrow

Posted 7 months ago

Question
There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____
Get tutor helpright-arrow

Posted 9 months ago

Question
There are two different raffles you can enter.\newlineIn raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are 1,0001,000 in the raffle, each costing `$11`.\newlineRaffle B is for a `$370` prize. Out of 125125 tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline[A]Raffle A\text{[A]Raffle A}\newline[B]Raffle B\text{[B]Raffle B}
Get tutor helpright-arrow

Posted 8 months ago

Question
XX is a normally distributed random variable with mean 4949 and standard deviation 2525.\newlineWhat is the probability that XX is between 2424 and 7474??\newlineUse the 0.68−0.95−0.9970.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.\newline____
Get tutor helpright-arrow

Posted 9 months ago

Question
XX is a normally distributed random variable with mean 6565 and standard deviation 88.\newlineWhat is the probability that XX is between 6262 and 6868??\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____
Get tutor helpright-arrow

Posted 9 months ago

Question
Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4343 and standard deviation 33, the bottom 30%30\% of the values are those less than ______.
Get tutor helpright-arrow

Posted 9 months ago

Question
Y Y is the number of desserts available in a randomly chosen restaurant.\newlineIs the random variable Y Y discrete or continuous?\newlineChoices:\newline[A]discrete \text{[A]discrete} \newline[B]continuous \text{[B]continuous}
Get tutor helpright-arrow

Posted 9 months ago

Question
Which of the following functions are continuous for all real numbers?\newlineg(x)=ln⁡(x) g(x)=\ln (x) \newlinef(x)=1x f(x)=\frac{1}{x} \newlineChoose 11 answer:\newline(A) g g only\newline(B) f f only\newline(C) Both g g and f f \newlineD Neither g g nor f f
Get tutor helpright-arrow

Posted 9 months ago

Question
Which of the following functions are continuous at x=−1 x=-1 ?\newlineg(x)=sin⁡(x+1) g(x)=\sin (x+1) \newlinef(x)=1x−1 f(x)=\frac{1}{x-1} \newlineChoose 11 answer:\newline(A) g g only\newline(B) f f only\newline(C) Both g g and f f \newline(D) Neither g g nor f f
Get tutor helpright-arrow

Posted 8 months ago

Question
Let g g be a continuous function on the closed interval [−1,4] [-1,4] , where g(−1)=−4 g(-1)=-4 and g(4)=1 g(4)=1 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) g(c)=−3 g(c)=-3 for at least one c c between −1-1 and 44\newline(B) g(c)=3 g(c)=3 for at least one c c between −4-4 and 11\newline(C) g(c)=−3 g(c)=-3 for at least one c c between −4-4 and 11\newline(D) g(c)=3 g(c)=3 for at least one c c between −1-1 and 44
Get tutor helpright-arrow

Posted 8 months ago

View all (21)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant