Maverick17
Maverick17
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Joined: Mar 4, 2011
March 4th, 2016 at 10:21:21 AM permalink
Please show your work, lol!

There are a series of contests with a 3 in 200 chance of winning each contest. There are 20 total contests.

200 tickets are sold for each contest, and there are three winners per contest, once a name is drawn, it cannot be drawn again for that contest.

You can theoretically win 20 times if you enter all (once per contest.)


Do my odds of winning change the more contests I enter? Not counting what I put in, what the value of the prize is, etc. Just the odds my name gets pulled at least once.
Statistics don't lie, they deceive.
rsactuary
rsactuary
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Joined: Sep 6, 2014
March 4th, 2016 at 10:47:52 AM permalink
If you enter one draw... the probability of winning is 3/200 = 0.015
If you enter two draws.. the probability of winning in at least one of them is 1-(197/200)^2 = 0.029
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If you enter twenty draws, the probability of winning at least one of them is 1-(197/200)^20 = .261

So the short answer is "yes".
RS
RS
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Joined: Feb 11, 2014
March 4th, 2016 at 10:50:37 AM permalink
Yes, the more contests you enter, the more likely you are to win at least one. If the 'house' has an advantage or takes a cut, then of course, it's better to not play at all (since you're then an expected loser).

Probability of winning at least one contest, where n is number of contests entered:
1 - [ (197/200) ^ n ]

https://www.google.com/search?q=1+-+(197%2F200)%5Ex&rlz=1C1CHWA_enUS609US609&oq=1+-+(197%2F200)%5Ex&aqs=chrome..69i57.284j0j7&sourceid=chrome&es_sm=93&ie=UTF-8
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