quasi
Posts:
12,050
Registered:
7/15/05


Re: Probability Pill
Posted:
Dec 27, 2012 6:45 AM


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

