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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

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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