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Sample Space Diagram


Date: 07/30/99 at 14:12:43
From: anonymous
Subject: Probability

Problem: In a human population 51% are male and 49% are female. 5% of 
the males and 0.3% of the females are colorblind. If a person randomly 
chosen from the population is found to be colorblind, what is the 
probability that the person is male?

I have attempted to solve this through the following set up:

     P(A1)   = .51     P(A2)= .49
     P(E/A1) = .5      P(E/A2)=.3

     P(E) = .5 * .51 + .49 * .3 = .402

Now what? None of this is making sense to me. Please help me out. 
Thank you ever so much.


Date: 07/30/99 at 16:37:57
From: Doctor Anthony
Subject: Re: Probability

A diagram is often a help with this sort of question

                 |      Male     |     Female      |  Total
       ----------|---------------|-----------------|---------
      Colorblind | .05*.51=.0255 | .0038.49=.00147 |
     Not colorbl.|     .4845     |                 |
       ----------|---------------|-----------------|---------
        Total    |      .51      |      .49        |   1.0

The entries in the above table can be entered from the information 
given. We can then complete the table so as to make row and column 
totals match the totals required.

                 |      Male     |     Female      |  Total
       ----------|---------------|-----------------|---------
      Colorblind | .05*.51=.0255 | .0038*49=.00147 | 0.02697
     Not colorbl.|     .4845     |     .48853      | 0.97303
       ----------|---------------|-----------------|---------
        Total    |      .51      |      .49        |   1.0

If the person is colorblind then the sample space is reduced to the 
top line with a total of 0.02697

                                    .0255
     Probability person is male  =  ------  =  0.945495
                                    .02697

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

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