Raffle winning odds (off topic)

W

Walter Mayes

This is off topic for this group but was hoping someone could give me an
answer.

Total tickets sold: 2000
Chances to win: 15
Tickets held: 20

Would my chances of winning a prize simply be 2000/15/20= 1 in 6.667 ?

The above seems logical but a little too simple. :)

Walter Mayes
 
B

Bernie Deitrick

Walter,

Well, that's not exactly how it is calculated, but it is not a bad estimate.

The easiest way to calculate the probability of winning at least one prize in a multi-prize raffle
is to calculate the probability of winning no prizes at all, and then subtract that value from 1:

Now, for the first draw, since you have 20 tickets, the probability of NOT winning the prize for
that draw is 1980/2000, or .99. But for the next, there are 1979/1999 ways to not win, or a
slightly less chance. If you extend that for 15 times, and multiply the results together, you get
0.8596, which means you have a 0.1404 chance of winning, or about 1 in 7 - very close to your
estimate.

But you can see that your estimate is better with fewer tickets. If you had 134 tickets, your calc
would have given a number greater than 100%, when in fact, you would have about a 75% chance of
winning at least once.

HTH,
Bernie
MS Excel MVP
 
B

bj

you are a little off,
use the
=HYPGEOMDIST(0,20,15,2000)
functionto find the probability of not winning at least one
subtract this from 1
your chance of winning at least one prize is 14.04 %

every time a non winning ticket is picked there are fewer tickets to pick from
so the the calc is (1985/2000*1984/1999*1983/1998* ... *1966/1981) for the
chance of not winning one out of twenty tickets.

The chance of winning a specific number of prizes is more complicated in
that you have to add the combo function since the winning ticket could be any
of your twenty
 
B

Bernie Deitrick

Sorry, I was being turned around. You would have about a 65% chance of winning at least one prize
if you held 134 tickets (out of 2000) in a 15 prize raffle, not 75%, which is your chance of winning
if there were 134 prizes with you holding 20 tickets....

Bernie
MS Excel MVP
 
W

Walter Mayes

Thank you Bernie and BJ. Your responses will "tax" this old grey head of
mine. :) I'll work through a few examples and hopefully get a spreadsheet
working.

Thanks
Walter Mayes
 
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