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Odds and Probability (A Heated Argument)


Date: 01/24/2001 at 11:05:08
From: mike
Subject: Odds and Probability (A Heated Argument)

I hope you can help me and explain something to me as simply as you 
possibly can. 

My friend and I are having a raffle. It has 40 prizes in it. If your 
name is drawn you go up and spin a wheel. You win the prize that the 
spot on the wheel lands on. If you win, your raffle ticket goes back 
into the hat and you are eligable to win again. There is not a limit 
on how many times you can win. 

My partner wants to have 8 spots on the wheel. He wants to start out 
with cheaper prizes and gradually move up to the more expensive 
prizes. This is where we disagree. I say that we should have all 40 
spots(prizes) on the wheel showing at all times, and if you hit a spot 
that has already won, you just spin again. This way everybody who has 
been lucky enough to have their raffle ticket drawn has a chance to 
win the big prizes. My partner says that everybody does have a chance 
to win the big prizes because their raffle tickets go back into the 
hat. 

He is basically saying that on each individual drawing you have a 
1/150 chance in winning. I say that is true on each individual 
drawing, but you cannot look at it that way. Your chances of winning 2 
or more times are more against you then you winning on any single 
drawing, and therefore if you win on the first drawing, you should be 
eligible for all prizes because it is greatly against you that you 
will win again. He says no, you still have a 1/150 chance, just like 
everybody else, on every drawing.


Date: 01/24/2001 at 11:53:46
From: Doctor Schwa
Subject: Re: Odds and Probability (A Heated Argument)

Hi Mike,

Your friend is right. As long as the tickets go back in the hat after 
they're drawn, and each of the 40 prizes is awarded exactly once to 
somebody, your chances of winning the big prize are the same 
regardless of whether your ticket has already been drawn.

The advantage of the "all on the wheel" system is that nobody knows
when the big prize is going to come, so they pay attention.  On the
other hand, if the first person to spin gets the big prize, then
everyone else will be less interested the rest of the time.

The advantage of the "put the big prizes on last" system is that
there's the suspense waiting for the end... but the disadvantage is
that people might not pay much attention at the beginning when only
the little prizes are up for grabs.

- Doctor Schwa, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Probability

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