# st: RE: RE: probability question

 From "Feiveson, Alan H. (JSC-SK311)" To "statalist@hsphsun2.harvard.edu" Subject st: RE: RE: probability question Date Wed, 28 Oct 2009 08:38:16 -0500

```The reason why I think the retrospective (i.e. finite sampling) approach is needed here is that we are given that it rains (rained?) exactly 7 of the days, not that the probability of rain is 7/120 on any given day.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Feiveson, Alan H. (JSC-SK311)
Sent: Wednesday, October 28, 2009 8:34 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: probability question

If you look at this retrospectively, you can use the hypergeometric distribution. Suppose we are given that it rained 7 of the 120 days and that the client wore the hat on 4 of those days. The probability that it rained on 3 of the four hat days would then be

(7C3 x 113C1 )/(120C4) = .00048146 (I think).

whew aCb refers to a things taken b at a time

Here "probability" refers to a repeated experiment in which one picks 4 of the 120 days at random to wear the hat, without knowledge of which of those are the rain days.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Richard Goldstein
Sent: Wednesday, October 28, 2009 7:38 AM
To: statalist
Subject: st: probability question

it's been a long time since I thought about questions like this, but, as
a lead-in to a study, a client has asked the following question which he
thinks he understands and says is related to where he wants to go:

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?

my client swears that this is not a homework problem for him or his wife
or one of their kids!

Rich
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