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September 1st, 2019, 10:18 AM   #1
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Very basic solution help.

Hello it has been a while since I have engaged mathematics formally. I am trying to determine my odds of winning a contest.

I had 1/300 chance of winning, and then received 1000 entries. This gave me 1/194 chance of winning. After receiving another 200 entries, I had a 1/181 chance of winning. Then, after another 420 entries, a 1/159 chance. Assuming the pool remains constant, how many entries must I submit to take my chances from 1/159 to 1/4 or 1/2 chance in winning.

Thank you.
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September 1st, 2019, 01:44 PM   #2
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Assuming it's like a raffle...
Let E be the original number of entries/tickets you had. Let T be the total number of entries in the pool.
The odds of winning are E/T.
So $\displaystyle \frac{E}{T} = \frac{1}{300}$
$\displaystyle \frac{E+1000}{T} = \frac{1}{194}$
$\displaystyle \frac{E+1200}{T} = \frac{1}{181}$
$\displaystyle \frac{E+1620}{T} = \frac{1}{159}$
You should be able to combine any two of these equations to solve for E and T.

$\displaystyle \frac{E+1000}{T} - \frac{E}{T}=\frac{1000}{T} = \frac{1}{194}-\frac{1}{300}=\frac{53}{29100} \rightarrow T=\frac{29~100~100}{53}\approx 549~057 \rightarrow E\approx 1830$
Accounting for the odds being rounded, this works out for the other numbers.

Therefore, you need roughly 137264 entries total for a 25.0 % chance of winning, or 274529 total for a 50.0 % chance of winning.
Thanks from romsek
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September 2nd, 2019, 08:04 AM   #3
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Thank you, Bones! Don't think I can accumulate that many, but I appreciate the work.
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