Re: [Phys-l] Marilyn does it again

[brian whatcott <betwys1@sbcglobal.net>]

On 12/25/2011 6:24 PM, John Mallinckrodt wrote:
> I think phys-l readers will get a kick out of today's "Ask Marilyn" column.  I think it is possible that she has never been so ludicrously wrong.
>
>     http://www.parade.com/askmarilyn/2011/12/Sundays-Column-12-25-11.html
>
> In fairness, I think it's pretty clear that the problem stems not from poor mathematical skills, but simply from astoundingly bad reading skills (likely amplified by her increasing tendency to phone it in.)  It seems pretty clear to me that she somehow managed to read the question as something more like, "IF a person has NOT been tested for a year, what is the probability that they will be tested the next time?"
>
> John Mallinckrodt
> Cal Poly Pomona
*[Questioner]
[In] an organization with 400 employees. Every three months, a 
random-number generator selects 100 names for testing. Afterward, these 
names go back into the selection pool. Obviously, the probability of an 
employee being chosen in one quarter is 25 percent. But what's the 
likelihood of being chosen over the course of a year? *

[Marilyn]
The probability remains 25 percent, despite the repeated testing.

****************************

Hmm, if a person was or was not chosen for testing in the last four 
periods, in the next period, her chance of being chosen is 25% This does 
not correspond with John's revisionist phrasing of the puzzle.
However, if a person was or was not chosen  in the last four test 
periods, her chance of being chosen in each of the NEXT four periods is 
indeed 25%.
However, her chance of NOT being chosen in ANY of the next four test 
periods is (1-0.25)^4 or 0.316 so her chance of being chosen at some 
point in the next four periods would be 1- 0.316 = 0.684

So the disputation turns on the reading of the phrase " [chance of] 
being chosen over the course of a year."   Is this to be taken as the 
cumulative chance, or rather the per-selection chance....

Brian W