Project: Raffle

Objective: Calculate probabilities and odds for a fund raising raffle.

Many churches, social organizations and schools use raffles as fund raisers. Study the raffle described below. Tickets cost $100.00. There are only 50,000 tickets available.

You Could be the Next Millionaire!


Buy a ticket in the Fall House of Dreams Charity Raffle for a chance to win a $1 Million Dream Home built anywhere in the U.S.A. or $1 Million cash! This is a chance to Change Your Life Forever. Enter the House of Dreams Raffle and win a house. Only 50,000 raffle tickets will be sold.

Charity House Raffle - Win a Million Dollar Dream House

or $1,000,000
Cash!

 

Win a Car - 2006 Cadillac STS or Mercedes SLK

or $50,000 CASH

 

or $25,000 CASH

 

Harley Davidson Motorcycle
Win a Harley Motorcycle - 2006 Harley Davidson Softail Deluxe

or $15,000 CASH

 

Win His and Hers Rolex Watches

or $10,000 CASH

 


Winner Selects $500 or One of the Following Prizes:

  • Samsung Digital Camera/Camcorder, 5 Megapixel DuoCam
  • Panasonic 9" Portable DVD Player 

 


Winner Selects $200 or One of the Following Prizes:

  • Polaroid Under the Counter 7" LCD TV
  • Supersonic DVD Home Theater System 

 


Winner Selects $100 or One of the Following Prizes:

  • Samsung DVD-VCR Player
  • Casio 2.5" LCD TV 

 

Use the raffle information to answer the following questions.
1.  Make a probability distribution table for this raffle.  Use the prize money as the events.  
     Remember to subtract the price of the ticket from the events when determining the 
     random variables.

2.  If all 50,000 tickets are sold, how much money will this charity make on their raffle?

3.  Using the prize money, not the random variable to define an event, find:
     A.  P(Winning the $1,000,000 Dream Home).

     B.  Odds against winning the $1,000,000 Dream Home.

     C.  Odds in favor of winning $50,000 or a Mercedes-Benz or a Cadillac.

     D.  P(Not Winning something).

     E.  Odds in favor of winning any prize.

     F.  P(Winning a prize worth at most $500).

     G.  P(Winning a prize worth more than $500).

     H.   P(Not winning a prize worth less than $200) 

     I.  Odds against winning a prize at least $200.

     J.  Are "winning $500" and "winning a prize" independent events?

     K.  P(Winning $500 | Won a prize)

     L.  Are "winning the $1,000,000 dream home" and "winning a prize" independent events?

     M.  P(Winning the $1,000,000 Dream Home | Won a prize)    

4.  Find the expected value of this raffle.

5.  How is the expected value related to the profit the charity makes on this raffle?

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