# Re: st: probability question

 From Richard Goldstein To statalist@hsphsun2.harvard.edu Subject Re: st: probability question Date Wed, 28 Oct 2009 10:13:45 -0400

```thank you!

Brian P. Poi wrote:
> 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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```