Sample Space DiagramDate: 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/ |
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