Expected value

Question

Imagine going to an electronics conference that is selling raffle tickets for $1 at the door. The prizes to be given away are: a $225 large flat screen television; two $75 MP3 players; and three $20 digital jump drives. Knowing that exactly 500 raffle tickets are sold, what is the expected value of each ticket you buy? (Use the cash value of the prizes along with their respective probabilities, and remember that a raffle ticket costs you $1.)

Answer 1

I am assuming that each prize will be given separately, and that you have no limit on how many you can win.

 

The "expected value" is the value of the prize times the probability of winning it.  Suppose the only prize is the TV for $225.  With 500 tickets sold, if you have one ticket, your chance of winning is 1/500.  The expected value is then $225 / 500 = $0.45

 

If you can win any or all of the prizes, then the expected value of your one ticket is cumulative.

 

TV:

p = 1/500, value = $225,  expected value = $0.45

 

MP3 Players:

p = 2/500, value = $75, expected value = $0.30

 

jump drives:

p = 3/500, value = $20, expected value = $0.12

 

Total expected value of 1 ticket is $0.87