# Re: st: probability question

 From Jeph Herrin To statalist@hsphsun2.harvard.edu Subject Re: st: probability question Date Wed, 28 Oct 2009 09:22:31 -0400

```
Prob(rain) = 7/120
Prob(no rain) = 113/120

X=days it rains on hat

Prob(X=3)=c(4,3)*(7/120)^3*(113/120)^1
=4*0.0001985*0.94
=0.0007477

not much chance!

Richard Goldstein wrote:
```
```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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