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September 1st, 2019, 11:18 AM  #1 
Newbie Joined: Sep 2019 From: Indiana Posts: 2 Thanks: 1  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. 
September 1st, 2019, 02:44 PM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 376 Thanks: 202 
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. 
September 2nd, 2019, 09:04 AM  #3 
Newbie Joined: Sep 2019 From: Indiana Posts: 2 Thanks: 1 
Thank you, Bones! Don't think I can accumulate that many, but I appreciate the work.


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