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Let's compare two different raffles to see which ticket you should buy? A. Raffle 1: 800 raffle tickets are sold $2.00 each. There is one gran prize for $450 and two consolation prizes of $100 each that will be awarded. What is the expected value of one ticket? B. Raffle 2: 350 raffle tickets are sold for $2.00 each. There is one grand prize of $150 and three consolation prizes of $50 each. What is the expected value of one ticket?

Respuesta :

MrRoyal

Answer:

(a) The expected value is: $0.40625

(b) The expected value is: $0.4286

Step-by-step explanation:

Solving (a): Raffle 1

Given

[tex]Tickets=800[/tex]

[tex]Value = \$2[/tex] per ticket

[tex]Grand\ Prize = \$450[/tex] ---- for 1

[tex]Consolation = \$100[/tex] --- for 2

Required

The expected value of each ticket

First, calculate the total amount of the 800 tickets

[tex]Amount = Tickets * Value[/tex]

[tex]A_1 = 800 * \$2[/tex]

[tex]A_1 = \$1600[/tex]

Next, calculate the total amount of the prizes

[tex]Amount = Tickets * Value[/tex]

[tex]A_2 = \$450 * 1 +\$100 * 2[/tex]

[tex]A_2 = \$450 +\$200[/tex]

[tex]A_2 = \$650[/tex]

The expected value E(x) of 1 ticket is calculated as:

[tex]E(x) = \frac{A_2}{A_1}[/tex]

[tex]E(x) = \frac{\$650}{\$1600}[/tex]

[tex]E(x) = \$0.40625[/tex]

Solving (b): Raffle 2

Given

[tex]Tickets=350[/tex]

[tex]Value = \$2[/tex] per ticket

[tex]Grand\ Prize = \$150[/tex] ---- for 1

[tex]Consolation = \$50[/tex] --- for 3

Required

The expected value of each ticket

First, calculate the total amount of the 800 tickets

[tex]Amount = Tickets * Value[/tex]

[tex]A_1 = 350 * \$2[/tex]

[tex]A_1 = \$700[/tex]

Next, calculate the total amount of the prizes

[tex]Amount = Tickets * Value[/tex]

[tex]A_2 = \$150 * 1 +\$50 * 3[/tex]

[tex]A_2 = \$150 +\$150[/tex]

[tex]A_2 = \$300[/tex]

The expected value E(x) of 1 ticket is calculated as:

[tex]E(x) = \frac{A_2}{A_1}[/tex]

[tex]E(x) = \frac{\$300}{\$700}[/tex]

[tex]E(x) = \$0.4286[/tex]

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