SOLUTION: In a test conducted it was found that of 1000 new recruits, 600 men and 400 women, 50 of the men and 4 of the women were red-green color-blind. Given that a recruit selected at r

Question 1186310: In a test conducted it was found that of 1000 new recruits, 600 men and 400
women, 50 of the men and 4 of the women were red-green color-blind. Given that
a recruit selected at random from this group is red-green color-blind, what is the
probability that the recruit is a male?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

            This text/problem seems to be complicated and twisted, but actually, it is quite simple.

            I will explain it to you now.

You have the big group of 1000 new recruits, = 600 men + 400 women.

Next, you have smaller group of 50 men + 4 women = 54 total, that are red-green color-blind.


You randomly select a person from this 54-persons group.
They ask you, what is the probability that this person is a male.


Now forget about this big/large group. The selection is done from the small group of 54 person,

and it is a reduced space of events.  The favorable event in this reduced space of events

is selecting a male. Obviously, the probability of this event is  


     =  = 0.9259.


It is the ANSWER to the problems question, and the problem is just SOLVED/COMPLETED.



Such kind of probabilities is called "conditional probability".

Instead of working with the total space of events (the big group), we reduce our consideration 

to the small group (the reduced space), where the actual choice is done.

There are different methods solving problems on "conditional probabilities".
Right now I told you about the simplest method.

In your further endeavors, if you will have another similar assignments, let me know,
and I will tell you about other methods.

If you are interested to make your knowledge wider and deeper on this subject, look into my lessons
    - Conditional probability problems
    - Conditional probability problems REVISITED
    - More problems on Conditional probability
in this site.

Read them to develop your skills and knowledge.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Solved problems on Probability"
and "Additional problems on Probability".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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