SOLUTION: You are given the following data Light smoker Smoker Men 50 200 Women 60 10 Find the probability that a person selected is man or light smoker,, Find the probability that a

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Question 1192432: You are given the following data
Light smoker Smoker
Men 50 200
Women 60 10
Find the probability that a person selected is man or light smoker,,
Find the probability that a person selected is woman or light smoker,,
Find the probability that a person selected is a smoker man,,
If a man is selected Find the probability that he is a smoker?

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Finish the chart by putting in the totals in a new
column on the right, and also in a new row on the
bottom.  When you add correctly across and down, 
you should get the same number in the bottom
right for both totals. In this case 320.
 
       ---------------------------------- 
       | Light smoker | Smoker | Totals |
-----------------------------------------
Men    |      50      |  200   |  250   |  
-----------------------------------------
Women  |      60      |   10   |   70   |
-----------------------------------------
Totals |     110      |  210   |  320   |
-----------------------------------------
Find the probability that a person selected is a man
or a light smoker,
I'll color red all the ones that are either a man or a light smoker:

       ---------------------------------- 
       | Light smoker | Smoker | Totals |
-----------------------------------------
Men    |      50      |  200   |  250   |  
-----------------------------------------
Women  |      60      |   10   |   70   |
-----------------------------------------
Totals |     110      |  210   |  320   |
-----------------------------------------

That's 50+200+60 = 310 out of 320, or 310/320,
which reduces to 31/32.

Find the probability that a person selected is woman or light smoker,

       ---------------------------------- 
       | Light smoker | Smoker | Totals |
-----------------------------------------
Men    |      50      |  200   |  250   |  
-----------------------------------------
Women  |      10      |   60   |   70   |
-----------------------------------------
Totals |     110      |  210   |  320   |
-----------------------------------------

That's 50+10+60 = 120 out of 320, or 120/320,
which reduces to 3/8.

Find the probability that a person selected is a smoker man,

       ---------------------------------- 
       | Light smoker | Smoker | Totals |
-----------------------------------------
Men    |      50      |  200   |  250   |  
-----------------------------------------
Women  |      60      |   10   |   70   |
-----------------------------------------
Totals |     110      |  210   |  320   |
-----------------------------------------

That's 200 out of 320, or 200/320,
which reduces to 5/8.

If a man is selected Find the probability that he is a smoker?
This one is different because we are given that a man is selected.
We were not given that in the others. So we eliminate the women
and the total, for the total includes the women.

       ---------------------------------- 
       | Light smoker | Smoker | Totals |
-----------------------------------------
Men    |      50      |  200   |  250   |  
-----------------------------------------
Women  |      60      |   10   |   70   |
-----------------------------------------
Totals |     110      |  210   |  320   |
-----------------------------------------

So this is just the 200 out of the 250, or 200/250,
which reduces to 4/5.

Edwin

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