Question

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. What is the expected value of this raffle if you buy 1​ ticket?

Answer 1

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:

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

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

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

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

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

Thus; the expected value of this raffle if you buy 1​ ticket = -0.65