Lincoln High School has 108 teachers. Of the 65 female teachers, 12 teach math.
1
6 of all the teachers teach math.

What is the probability that a teacher is a man or does not teach math?

Question

Lincoln High School has 108 teachers. Of the 65 female teachers, 12 teach math. 
1
6 of all the teachers teach math.

What is the probability that a teacher is a man or does not teach math?

anonymous · Answer

Is that "1/6" of all teachers teach math?

anonymous · Answer

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18 comes from 1/6 of 108.  So there are 18 Math teachers, leaving only 6 that are male.  There are 108 teachers total, 65 of whom are female, leaving 43 male teachers.  The other numbers are easy to fill in after that.

The number of people who don't teach Math are: 90.  That includes some of the males already.  To get the other males, we have to look at the males who do actually teach Math, of which there are 6.  So, the number of people who do not teach Math or who are male is:

90 + 6 = 96

Your probability is:   96/108    =   8/9

anonymous · Answer

Another way to do this is simply look to see the number of "female and Math teacher".  There are 12 of those out of 108, which is 1/9.  You can then take for your answer:

1 - 1/9 = 8/9

anonymous · Answer

All good now, @wequess2 ?   Those are 2 ways to do the problem.  I actually like the second way better because it is shorter and quicker.  Your group of selection is anyone but "female and Math teacher".  That leaves everyone but the 12 female Math teachers which is 96.  Pick either way (or both) that you like.