Date: Dec 27, 2012 6:45 AM
Author: quasi
Subject: Re: Probability Pill
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