The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $3. There is 1 winning ticket out of th

Question

The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $3. There
is 1 winning ticket out of the 300 tickets sold. The winner gets a prize worth $62. Round your answers
to the nearest cent.

What is the expected value (to you) of one raffle ticket? $

Calculate the expected value (to you) if you purchase 6 raffle tickets. $

What is the expected value (to the PTO) of one raffle ticket? $

If the PTO sells all 300 raffle tickets, how much money can they expect to raise for the classroom
supplies? $

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Mộc Miên 4 years 2021-08-02T07:40:07+00:00 1 Answers 221 views 0

Answers ( )

  1. kimcuc
    0
    2021-08-02T07:41:26+00:00
    Reply

    Answer:

    Suppose that in a given event, there are N outcomes:

    {x₁, x₂, …, xₙ}

    Such that the probabilities are:

    {p₁, p₂, …, pₙ}

    The expected value is:

    EV = x₁*p₁ + x₂*p₂ + … + xₙ*pₙ

    In this case, we know that each ticket costs $3.

    There is 1 winning ticket out of 300 tickets, where the prize is $62.

    Then we have two events, the one where you win.

    x₁ = $62 – $3 = $59

    With a probability:

    p₁ = 1/300

    The one where you don’t win (and still pay for the ticket):

    x₂ = -$3

    p₂ = 299/300

    a) Then the expected value is:

    EV = ( 1/300)*$59 + (299/300)*(-$3) = -$2.79

    b) The expected value is additive, this means that if you buy 6 tickets, the expected value will be equal to 6 times the expected value of a single ticket.

    EV = 6*(-$2.79) = -$16.74

    c) For the PTO the events are:

    Winner ticket, so you lose $62 and win $3 for selling the ticket.

    x₁ = $3  – $62 = -$59

    p₁ = 1/300

    Normal ticket, you win $3.

    x₂ = $3

    p₂ = 299/300

    In this case the expected value is:

    EV = (1/300)*(-$59) + (299/300)*$3 = $2.79

    d) If the PTO sells the 300 tickets, then the expected value is 300 times the expected value for a single ticket:

    EV = 300*$2.79 = $837

    We should have the exact same than selling the 300 tickets:

    300*$3 = $900

    minus the $62 for the price:

    $900 – $62 = $838

    There is a difference of $1, that happens because we rounded the value of the expected value (the actual one was $2.792…)

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