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Re: st: probability question


From   "Brian P. Poi" <bpoi@stata.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: probability question
Date   Wed, 28 Oct 2009 09:03:47 -0500 (CDT)

On Wed, 28 Oct 2009, Richard Goldstein wrote:


during a consecutive period of 120 days, if it rains on 7 days and my
client wears a hat on 4 days (these are independent of any knowledge of
the weather), what is the probability that it will rain on 3 of the days
on which he is wearing a hat?


Perhaps beating Maarten to the punch, I immediately thought to do a simulation, and I came up with 0.00048260, right in line with Al Feiveson's analytic solution.

----------------------------------------
mata:

rseed(1)
tries = 10000000
totaln = 0
for(i=1; i<=tries; ++i) {

	// rain has 7 ones
	rain = J(120, 1, 0)
	rain[1..7] = J(7,1,1)

	// hat has 4 ones
	hat = J(120, 1, 0)
	hat[1..4] = J(4,1,1)

	// shuffle each one
	_jumble(rain)
	_jumble(hat)

	// if there's a match, hat+rain==2
	both = rain + hat
	matches = sum(both:==2)
	// we want to know if there were three matches
	if (matches == 3) {
		totaln = totaln + 1
	}
	if (mod(i, 1000) == 0) {
		printf(".")
	}
}


printf("\n\nProbability is about %10.8f\n", totaln/tries)

end
----------------------------------------


  -- Brian Poi
  -- bpoi@stata.com
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