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# more fun with coins

Best Answer bonanova, 27 April 2014 - 05:53 AM

Suppose John tosses a coin 250 times and Eric tosses a coin 251 times, what is the probability that john's coin has more heads than Eric?  What is the probability that Eric has more heads than John?

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9 replies to this topic

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Posted 11 April 2014 - 07:51 PM

Suppose John tosses a coin 250 times and Eric tosses a coin 251 times, what is the probability that john's coin has more heads than Eric?  What is the probability that Eric has more heads than John?

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### #2 Rob_G

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Posted 11 April 2014 - 08:39 PM

Spoiler for I'd say Eric...

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### #3 bonanova

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Posted 13 April 2014 - 07:53 AM

Spoiler for Looks like

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Vidi vici veni.

### #4 Rob_G

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Posted 14 April 2014 - 04:13 PM

Spoiler for I think John has

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Posted 15 April 2014 - 01:19 AM

Spoiler for I think John has

Why?
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### #6 Rob_G

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Posted 15 April 2014 - 04:26 PM

Spoiler for I think John has

Why?

Spoiler for My reasoning...

Spoiler for As a side note

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### #7 dgreening

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Posted 23 April 2014 - 02:22 PM

Spoiler for
Another perspective

I suspect that the impact of the extra toss is actually very small and it could go either way.

For 250 [or 251] tosses, you would expect some sort of distribution centered heavily around 50% [or 125 heads].

This is not even close to being a uniform distribution, so most points below 110 or above 140 are zero. [just a guess on the end points]. The point is that there are really only a small number of points that have to be considered.

Another approach might be to do some sort of convolution of the 2 distributions [which look virtually identical].

Since Ties go to John, the probabilityt will be less than 50%

Rob G may be pretty close [I am not sure].

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### #8 dgreening

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Posted 23 April 2014 - 02:35 PM

Spoiler for

Edited by dgreening, 23 April 2014 - 02:37 PM.

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### #9 dgreening

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Posted 23 April 2014 - 02:59 PM

Edited by dgreening, 23 April 2014 - 03:00 PM.

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### #10 bonanova

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Posted 27 April 2014 - 05:53 AM   Best Answer

Suppose John tosses a coin 250 times and Eric tosses a coin 251 times, what is the probability that john's coin has more heads than Eric?  What is the probability that Eric has more heads than John?

Spoiler for Looks like

• 0

Vidi vici veni.

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