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

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


"Walter Mayes" wrote in message
...
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

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

"Walter Mayes" wrote:

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

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


"Bernie Deitrick" <deitbe @ consumer dot org wrote in message
...
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


"Walter Mayes" wrote in message
...
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

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


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

"Walter Mayes" wrote:

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