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### Conditional Probability

```
Date: 05/25/2000 at 17:33:01
From: Faraz Sultan
Subject: Probability and Logic

Hi Dr. Math.

I'm going crazy over this problem I haven't been able to figure out -

Suppose used car salesmen tell the truth 2/5 of the time, and 1/3 of
the trees in a forest are oak. If 4 used car salesmen say that a
certain tree in the forest is oak, what is the probability that the
tree is indeed oak?

I thought the answer would be [(2/5)^4]*[1/3], but that gave me an

Please show me how this can be determined.

Thanks a lot,
Faraz
```

```
Date: 05/25/2000 at 19:19:09
From: Doctor Anthony
Subject: Re: Probability and Logic

Hi Faraz:

Oak                    Not oak
Prob = 1/3              Prob = 2/3
-------------------------------------------
(1/3).C(4,4)(2/5)^4      (2/3).C(4,0)(3/5)^4     4 say it is oak
= 16/1875                 162/1875            Total = 178/1875

Probability that we are in the first column

16/1875      16      8
=  --------  =  ---  =  --  =  0.08988764
178/1875     178     89

and so probability that it is oak = 8/89

- Doctor Anthony, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Probability
High School Probability

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