Expert: Paul Klarreich - 4/17/2007

Question
a study indicates that 5% of men and 0.5% of women are colorblind.  find the probility of choosing a colorblind man and and then another colorblind man. assume that the two events are independent.

Answer
Questioner:   dillon
Category:  Advanced Math
Private:  No   << Good for you!
 
Subject:  math << Not so good.  A good subject line tells something about the example.

Question:  a study indicates that 5% of men and 0.5% of women are colorblind.  find the probability of choosing a colorblind man and and then another colorblind man. assume that the two events are independent.
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Hi, Dillon,

Basic principle:  If events A and B are independent, then:

p(A AND B) = p(A) p(B)

So in this case, if
A = "choose a colorblind man" and
B = "choose another"

p(A) = 0.05
p(B) = 0.05
p(A AND B) = 0.05 * 0.05 = 0.0025

Warning: If you change the conditions of the problem to something like this:

In 100 men, 5 are colorblind.  Find the probability of first choosing a colorblind man and and then another colorblind man from those remaining.

Now the assumption of independence is incorrect.  This is called 'selection without replacement' and is slightly different.

>> I am glad you paid attention to my request that you not use the Private flag.  Here's my next request:  Your computer's keyboard has these large keys in the main area labeled "Shift".  You should make judicious use of them such as, for example, to capitalize the first letter of a new sentence, but not, of course, to write EVERYTHING IN CAPS LIKE THIS, which is like shouting.