# Re: st: RE: RE: probability question

 From Jeph Herrin To statalist@hsphsun2.harvard.edu Subject Re: st: RE: RE: probability question Date Wed, 28 Oct 2009 10:36:36 -0400

```Good point. Sampling without replacement, versus (my solution)
sampling with replacement.

J

Feiveson, Alan H. (JSC-SK311) wrote:
```
```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!

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```
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