Problem 1
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Explanation:
The notation "P(tune-ups | AC repair)" is the same as saying "P(tune-ups given AC repair)".
The "given" means we only focus on the "AC repair" circle.
Add up the numbers in that circle to get: 1+3+2+0 = 6
There are 6 ASE certified mechanics that can do AC repair.
Of those 6 people, only 2+0 = 2 can do engine tune-ups. Note I added the values in the "AC repair" and "tune-ups" overlapped region.
Therefore, we get the probability 2/6 = 1/3
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Problem 2
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Explanation:
First, we'll add the numbers found in either the "brakes" or "tune-ups" circles.
4+1+2+2+3+0 = 12
There are 12 mechanics that can handle brakes or tune-ups or both.
Now add up all of the numbers shown regardless of their location. We have 4+1+3+2+2+0+3+3 = 18 mechanics total.
So,
m = number who can do brakes or tune-ups or both
m = 12
n = number of mechanics total
n = 18
And,
P(brakes or tune-ups) = m/n
P(brakes or tune-ups) = 12/18
P(brakes or tune-ups) = (6*2)/(6*3)
P(brakes or tune-ups) = 2/3
