Proj: Raffle Stat. Answers

There are 445 winners in this raffle. There are 40,000 tickets sold in this raffle. 445 / 40,000 = 0.011125. The sample is at most 5%. Independence can be assumed.

2. 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. Write out all the decimal places.

Event	x	Freq	P(x)	x * P(x)
$1,000,000	$999,900	1	0.000025	$24.9975
$35,000	$34,900	1	0.000025	$0.8725
$25,000	$24,900	1	0.000025	$0.6225
$15,000	$14,900	1	0.000025	$0.3725
$10,000	$9,900	1	0.000025	$0.2475
$150	$50	60	0.0015	$0.075
$130	$30	60	0.0015	$0.045
$100	$0	60	0.0015	0
$90	-$10	60	0.0015	-$0.015
$120	$20	50	0.00125	$0.025
$110	$10	50	0.00125	$0.0125
$90	-$10	50	0.00125	-$0.0125
$80	-$20	50	0.00125	-$0.025
0	-$100	39,555	0.988875	-$98.8875
Total		40,000	1.000000	-$71.67

3. If all 40,000 tickets are sold, how much money will this charity make on their raffle?
Revenue - Costs = Profit
Revenue = (40,000 tickets) *$100 / ticket = $4,000,000

     Costs = Sum of all prizes
     Costs = $1,000,000 + $35,000 + $25,000 + $15,000 + $10,000 + 60 * $150 + 60 * $130 +
                   60 * $100 + 60 * $90 + 50 * $120 + 50 * $110 + 50 * $90 + 50 * $80 = $1,133,200

4. Using the prize money, not the random variable to define
an event, find:
A. P(Winning the $1,000,000 Dream Home). 1 / 40,000 = 0.000025 = 0.0025%

B. Odds against winning a Homedics Wireless Speakers and Ipod Deck. Losers : Winners 39,940 : 60

C. Odds in favor of winning a Samsung 4Gb Multimedia Player. Winners : Losers 50 : 39,950

D. P(Not Winning any prize). There are 445 prizes. There are 40,000 - 445 = 39,555 losers
39,555 / 40,000 = 98.8875%

E. Odds in favor of winning any prize. There are 445 prizes. There are 40,000 - 445 = 39,555 losers
Winners : Losers 445 : 39,555

F. P(Winning a prize worth at most $100). There are 220 prizes worth $100 or less.
220 / 40,000 = 0.0055 = 0.55%

   G. P(Not winning a prize worth more than $100).
            Hint: Losing is included.
            P(Not winning a prize worth more than $100) = 1 - P(Winning a prize worth more than $100).
            There are 225 prizes worth more than $100.        225 / 40,000 = 0.005625 = 0.5625%
            1 - 0.005625 = 0.994375 = 99.4375%

H. Odds in favor of winning a prize worth less than $120. There are 270 prizes worth less than $120.
40,000 - 270 = 39,730 Winners : Losers 270 : 39,730

I. Odds against winning a prize at least $120. There are 175 prizes worth $120 or more.
40,000 - 175 = 39,825 Losers : Winners 39,825 : 175

     J. P(Losing money on the Raffle)
          Hint: Losing or winning a prize worth less than $100 is losing money.
          There are 39,715 people who either loss or won prizes worth less than $100.
          39,715 / 40,000 = 0.992875 = 99.2875%.

     K. Are "Winning a Homedics Wireless Speakers and Ipod Deck" and "Winning a prize" independent events?
           If P(Winning a Homedics System) times P(Winning a prize) = P(Winning Homedics System and Winning a prize)
         Then the events are independent.
         P(Winning a Homedics System) times P(Winning a prize) = (60 / 40,000) (445 / 40,000) approximately 0.0000166875.
           P(Winning a Homedics System and winning a prize) = P(Winning a Homedics System) = 60 / 40,000 approximately
           0.0015.
           The products are not equal. The events are dependent.

L. P(Winning a Homedics Wireless Speakers and Ipod Deck. | Winning a prize).
(60 / 40,000) / (445 / 40,000) = 60 / 445 approximately 0.134831461.

6. How is the expected value related to the profit the charity makes on this raffle?
-$71.67 is the money loss, on an average, by each ticket buyer. This is the money gained by the charity
for each ticket sale.