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Topic: Probability Pill
Replies: 20   Last Post: Jan 31, 2013 7:23 PM

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quasi

Posts: 10,208
Registered: 7/15/05
Re: Probability Pill
Posted: Dec 27, 2012 6:45 AM
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quasi wrote:
>quasi wrote:
>>quasi wrote:
>>>William Elliot wrote:
>>>

>>>>Each day I take 1/2 an aspirin tablet. I bought a bottle of
>>>>100 tablets; each day I take out one, if it's whole I break
>>>>it half and eat a half and put the other half back: if I pull
>>>>out a half tablet I eat it. I was wondering after I break the
>>>>last whole one what the expected number of halves are in the
>>>>bottle? I assume that any piece I pull out has uniform
>>>>probability.

>>>
>>>I suspect that the above question is not actually yours.
>>>
>>>If that's the case, what is the actual source?
>>>
>>>Is it from a poster in another forum? If so, why do you omit
>>>mention of the poster and the forum?
>>>
>>>Is it from a book or math contest?
>>>
>>>Why do you repeatedly post questions that are not your own
>>>without giving credit to the source?
>>>
>>>In any case, the expected number of halves left when the last
>>>whole pill is split is
>>>
>>> (199!) / ((4^99)*((99!)^2))

>>
>>Which is slightly more than 11 half pills.

>
>Oops -- ignore my answer -- it's blatantly wrong.
>
>I'll rethink it.
>
>In the meantime, can you identify the source of the
>problem?


Ok, the correct answer is x/y where x,y are given by

x = 14466636279520351160221518043104131447711

y = 2788815009188499086581352357412492142272

As a decimal, x/y is approximately 5.18737751763962

Thus, on average, about 5 half pills.

quasi



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