Answer:
the expected value of this raffle if you buy 1 ticket = -0.65
Step-by-step explanation:
Given that :
Five thousand tickets are sold at $1 each for a charity raffle
Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $500, 3 prizes of $300, 5 prizes of $50, and 20 prizes of $5.
Thus; the amount and the corresponding probability can be computed as:
Amount 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 if 1 ticket is being bought is as follows:
[tex]E(x) = \sum x * P(x)[/tex]
[tex]E(x) = (499 * \dfrac{1}{5000} + 299 *\dfrac{3}{5000} + 49 *\dfrac{5}{5000} + 4 * \dfrac{20}{5000} + (-1 * \dfrac{4971}{5000} ))[/tex]
[tex]E(x) = (0.0998 + 0.1794+0.049 + 0.016 + (-0.9942 ))[/tex]
[tex]E(x) = (0.3442 -0.9942 )[/tex]
[tex]\mathbf{E(x) = -0.65}[/tex]
Thus; the expected value of this raffle if you buy 1 ticket = -0.65
