Math CentralQuandaries & Queries


Question from Katrina, a student:

9% of men and .25% of woman can't distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic lights. If 6 men are randomly selected for a study of traffic signal perceptions, find the probability that exactly two of them cannot distinguish between red and green.

Hi Katrina.

How many ways can you choose 2 men from among 6? You have six choices for the first man and five for the second, so there are 6 x 5 / 2 = 15 different pairs. You might know the notation 6C2 = 6! / ( 2! x (6-2) ! ) = 6 x 5 / 2 = 15.

Now if the first two men are color blind and the next four are not, there is a 0.09 x 0.09 x 0.91 x 0.91 x 0.91 x 0.91 chance of that. So the answer to your question is the product of all this:

6C2 x 0.092 x 0.914

Hope this helps,
Stephen La Rocque.

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