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 - 
please help.

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 
incorrect answer. (Answer ~= .08989)

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/