SOLUTION: The probability that a randomly selected elementary or secondary school teacher from a city is a female is 0.66, holds a second job is 0.46, and is a female and holds a second job

Question 1083738: The probability that a randomly selected elementary or secondary school teacher from a city is a female is 0.66, holds a second job is 0.46, and is a female and holds a second job is 0.22. Find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job.
-I've tried just about every way and I only have one more submission left on my homework to get it right. The most recent I did was [.66 + .46 - (.119)= .84 ] that was incorrect. I know I'm using the right formula P(A or B) = P(A) + P(B) - P(A and B)
Found 2 solutions by KMST, MathLover1:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would say that P(A and B) = 0.22 was given to you directly.
That gives you P(A or B) = 0.66 + 0.46 - 0.22 = 0.90 .
Adding 0.66+0.46 you get all female teachers l
plus all teachers with a second job,
but that would be counting twice all female teachers with a second job,
so you have to subtract the 0.22 that is female and works 2 jobs,

You do not need to rely on formulas if you can use common sense.
You can imagine the situation, and if you were a newspaper reporter,
you would be interviewing some of those teachers for the human side of the story.
Say there are 100 teachers.
Of those, 66 are women. (The other 34 must be men).
There are 22 female teachers with a second paid job.
(They must be early in their careers, so they are poorly paid,
and they are not supported by anyone else, so they need the extra income).
The other 66-22=44 women teachers do not have a second job.
(Some are paid very well because of seniority and having extra education;
some are married to successful lawyers and doctors).
There are 46 teachers that have a second job.
Those must include the 22 female teachers who have a second job,
but the other 46-22=24 must be male.
They are 24 of the 34 male teachers who have no wife bringing home money,
and need that second job to make ends meet. It's a rough life.
So, you have only 34-24=10 male teachers who do not have a second job.
Those are the lucky ones.
The other 100-10=90 teachers are women who work hard at home when not teaching,
or have a second job, or both.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

J = holds a 2nd job
P(F or J) = P(F) + P(J) - P(F & J) =
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