Problema Solution
Five thousand raffle tickets are being sold to raise money for a school trip. The tickets cost $5. There will be three prizes drawn, one will be for $5,000 and the other two will be for $500. What is the expected value for this raffle? Remember that everyone needs to buy a ticket, and the winner will need to subtract the cost of the ticket from their winnings. Also, assume that all tickets have an equal chance of being selected.
Answer provided by our tutors
expected value is calculated as the sum of all possible values each multiplied by the probability of its occurrence
In this problem there are 3 outcomes: win grand prize, win second prize, win nothing.
Outcome 1: win grand prize of $5,000
there are 1000 tickets but only 1 winner, so p = 1/1000 = 0.001 is the probability of this outcome
you win $5,000 but it cost you $5, so g = 5000 - 5 = $4995
Outcome 2: win second prize of $500
there are 1000 tickets and only 2 winners, so p = 2/1000 = 1/500 = 0.002 is the probability of this outcome
you win $500 but it cost you $5, so g = 500 - 5 = 495
Outcome 3: win nothing
1000-2-1=997, this means 997 tickets do not win, so p = 997/1000 = 0.997
you win 0 but it cost you $5, so g = 0-5 = -5
The Expected Value (EV) is:
EV = 0.001*4995 + 0.002*495 + 0.997*(-5)
EV = $1
the expected value is $1.