SOLUTION: The Organic Mattress Company, makers of the Savvy and Reverie type mattress, is conducting a raffle. The proceeds will go to the Sleep Apnea Foundation. The cost of a ticket is

Algebra ->  Finance -> SOLUTION: The Organic Mattress Company, makers of the Savvy and Reverie type mattress, is conducting a raffle. The proceeds will go to the Sleep Apnea Foundation. The cost of a ticket is      Log On


   

Question 1086150: The Organic Mattress Company, makers of the Savvy and Reverie type mattress, is conducting a raffle. The proceeds will go to the Sleep Apnea Foundation. The cost of a ticket is $ 20 ( tax deductible). The prizes are as follows: One (PRIZE )deluxe mattress set valued at $ 4,999; two (PRIZES) standard mattress sets valued at 2,499 EACH and a budget set valued at $ 1,555. There are 4 prizes ! NUMBER OF TICKETS SOLD IS 1000. find the expected value of this raffle.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The expected value is E(X) = SIGMAXi*Pi, where Xi is the value of the i-th outcome and Pi is the probability of the i-th outcome.
There are 4 possible outcomes:
1. You win the deluxe set valued at $4999
2. You win the standard set valued at $2499
3. You win the budget set valued at $1555
4. You lose $20 (cost of the ticket)
For each of the prizes, we have to deduct the cost of the ticket from the value
The probability for the 4 outcomes is:
1. P(deluxe) = 1/1000 [1 prize]
2. P(standard) = 2/1000 [2 prizes]
3. P(budget) = 1/1000 [1 prize]
4. P(lose) = 996/1000
Therefore E(X) = (1/1000)*$4979 + (2/1000)*$2479 + (1/1000)*$1535 + (996/1000)*$20 = -$8.45