SOLUTION: P(A'n B) = 0.22 and P(A' n B') - 0.18 Find P(A) and P(A u B)

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Question 992130: P(A'n B) = 0.22 and P(A' n B') - 0.18
Find P(A) and P(A u B)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
P(A' ᑎ B) = 0.22 and P(A' ᑎ B') = 0.18

Find P(A) and P(A ᑌ B)

It's complicated using formulas. The easy way is 
with an Euler-Venn diagram:



We are given the probabilities of two of the regions,
1. the right region of B, the blue circle, as 0.22.
2. the region outside both circles but inside the
rectangle, as 0.18.

The two regions we are not given the probability of
make up A, the entire red circle.

The probabilty of the union of the two regions outside of
A is 0.22 + 0.18 = .40.

So P(A) = 1 - 0.40 = 0.60  

A ᑌ B is made up of both regions of A and the right region
of B,

So P(A ᑌ B) = 0.60 + 0.22 = 0.82

Edwin