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 gr

Question

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?

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Diễm Thu 7 months 2021-07-19T00:47:34+00:00 1 Answers 3 views 0

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    2021-07-19T00:49:12+00:00

    Answer:

    (a) The expected value is: $0.40625

    (b) The expected value is: $0.4286

    Step-by-step explanation:

    Solving (a): Raffle 1

    Given

    Tickets=800

    Value = \$2 per ticket

    Grand\ Prize = \$450 —- for 1

    Consolation = \$100 — for 2

    Required

    The expected value of each ticket

    First, calculate the total amount of the 800 tickets

    Amount = Tickets * Value

    A_1 = 800 * \$2

    A_1 = \$1600

    Next, calculate the total amount of the prizes

    Amount = Tickets * Value

    A_2 = \$450 * 1 +\$100 * 2

    A_2 = \$450 +\$200

    A_2 = \$650

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

    E(x) = \frac{A_2}{A_1}

    E(x) = \frac{\$650}{\$1600}

    E(x) = \$0.40625

    Solving (b): Raffle 2

    Given

    Tickets=350

    Value = \$2 per ticket

    Grand\ Prize = \$150 —- for 1

    Consolation = \$50 — for 3

    Required

    The expected value of each ticket

    First, calculate the total amount of the 800 tickets

    Amount = Tickets * Value

    A_1 = 350 * \$2

    A_1 = \$700

    Next, calculate the total amount of the prizes

    Amount = Tickets * Value

    A_2 = \$150 * 1 +\$50 * 3

    A_2 = \$150 +\$150

    A_2 = \$300

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

    E(x) = \frac{A_2}{A_1}

    E(x) = \frac{\$300}{\$700}

    E(x) = \$0.4286

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