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2 months ago

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Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded a

s follows: 1 prize of $500, 3 prizes of $300, 5 prizes of $50, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?

1 answer:

babunello [11.8K]2 months ago

7 0

Response:

the expected value of this raffle if you purchase 1 ticket = -0.65

Breakdown of the calculation:

Details:

5,000 tickets are sold at $1 each for a charitable raffle

Winners will be chosen at random with cash prizes as follows: 1 prize of $500, 3 prizes of $300, 5 prizes of $50, and 20 prizes of $5.

Therefore, the value and its respective probability can be calculated as follows:

Value Probability

$500 - $1 = $499 1/5000

$300 - $1 = $299 3/5000

$50 - $1 = $49 5/5000

$5 - $1 = $4 20/5000

-$1 1 - 29/5000 = 4971/5000

The expected value of the raffle when buying 1 ticket is computed as follows:

$E(x) = \sum x * P(x)$

$E(x) = (499 * \dfrac{1}{5000} + 299 *\dfrac{3}{5000} + 49 *\dfrac{5}{5000} + 4 * \dfrac{20}{5000} + (-1 * \dfrac{4971}{5000} ))$

$E(x) = (0.0998 + 0.1794+0.049 + 0.016 + (-0.9942 ))$

$E(x) = (0.3442 -0.9942 )$

$\mathbf{E(x) = -0.65}$

So, the expected value of this raffle when one ticket is purchased = -0.65

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