Expert: Paul Klarreich - 12/19/2008

Question
Hi,

This question is about the probability that a specific door prize (one of 20) would be won by a specific individual (out of 120 persons).  

We had a holiday party last night.  120 people attended, and each received a number.  during the evening 20 door prizes were given out.  Per the usual practice, if someone won a prize, it would not be possible for them to win another prize because their number was NOT returned to the hat.  One of our guests donated one door prize.  To everyone's surprise, our guest's number was drawn as the winning number when the prize she donated was the item being given away (she did not accept the prize).  

What are the odds that at the beginning of the evening --  before the drawings started -- that our guest would be the person to win the door prize she donated?  

Thanks for your help.

Answer
Questioner:   Mel
Category:  Advanced Math
 
Subject:  Probability -- door prize
Question:  Hi,

This question is about the probability that a specific door prize (one of 20) would be won by a specific individual (out of 120 persons).  

We had a holiday party last night.  120 people attended, and each received a number.  during the evening 20 door prizes were given out.  Per the usual practice, if someone won a prize, it would not be possible for them to win another prize because their number was NOT returned to the hat.  One of our guests donated one door prize.  To everyone's surprise, our guest's number was drawn as the winning number when the prize she donated was the item being given away (she did not accept the prize).  

What are the odds that at the beginning of the evening --  before the drawings started -- that our guest would be the person to win the door prize she donated?  

Thanks for your help.
....................................
Hi, Mel,

Why isn't it just 1/120?  There are 120 people and ONE PRIZE.  You did say, 'before the drawings started', didn't you?

We think there were 20 prizes, but in fact the prizes consisted of  one Mercedes E350 automobile and 19 coupons for a free tube of ketchup at McDonald's -- so who cares about the other so-called prizes?

Now if the person donating the Mercedes won it, I would be inclined to think the probability was 100% (and call the local D.A.) but that is another issue.