Date: Dec 28, 2012 4:29 PM Author: quasi Subject: Re: Probability Pill 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?

Based on the results of a web search, it's almost certain that

William Elliot got the problem from an outside source. There's

nothing wrong with that, but I think he should then at least

attribute the problem to his source.

William's question is a special case of problem E3429 in the

April 1991 issue of the American Mathematical Monthly. It was

proposed by Donald Knuth and John McCarthy and was solved in a

later issue. The AMM editors indicate that the some of the

solvers were already familiar with the problem. I quote the

AMM editors:

Robert High saw a version of it in the MIT Technology

Review of April, 1990. Helmut Prodinger reports that he

proposed it in the Canary Islands in 1982. Daniel Moran

attributes the problem to Charles MacCluer of Michigan

State University, where it has been known for some time.

A detailed discussion of the problem can be found in one of

David Pollard's course handout on expectation:

<http://www.stat.yale.edu/~pollard/Courses/241.fall2011/YaleOnly/notes2011/Expectation.pdf>

See example 7 starting on page 17 and continuing through page 22.

But here's my guess as to how William got the problem ...

A student, unaware of the origin of the problem, received

the problem as a HW problem (possibly a challenge problem

for extra credit) and posted the problem in some forum,

asking for a solution. William then posted the question

to sci.math, with no attribution as to his source.

If solutions had appeared in sci.math, William would

presumably have posted a solution back to the forum where

he first saw the question. But in doing so, would William

have mentioned the source of his solution, giving credit

to the solver? I wonder.

But the above is just a guess.

So William, tell us -- what's the real story?

quasi