I have a couple of questions on this problem.

P[AuB]=0.7 and P[AuB']=0.9

Determine P[A]

I understand the substitution via Disjunction Rule to:

P[AuB]=P[A]+P[B]-P[AnB]

P[AuB']=P[A]+P[B']-P[AnB']

Then combining the terms to:

P[AuB]+P[AuB']=2P[A]+(P[B]+P[B'])-(P[AnB]+P[AnB'])

But, the next part seems like hand waving on the right-hand side of the equation.

0.7+0.9=2P[A]+1-P[(AnB)u(AnB')]

How do we get to 1-P[(AnB)u(AnB')] from (P[B]+P[B'])-(P[AnB]+P[AnB'])?

The next step suggests:

1.6=2P[A]+1-P[A] and subsequently P[A]=0.6

Also, is there any notable difference between B' (B prime?) and say C or any other variable. Thanks in advance.

P[AuB]=0.7 and P[AuB']=0.9

Determine P[A]

I understand the substitution via Disjunction Rule to:

P[AuB]=P[A]+P[B]-P[AnB]

P[AuB']=P[A]+P[B']-P[AnB']

Then combining the terms to:

P[AuB]+P[AuB']=2P[A]+(P[B]+P[B'])-(P[AnB]+P[AnB'])

But, the next part seems like hand waving on the right-hand side of the equation.

0.7+0.9=2P[A]+1-P[(AnB)u(AnB')]

How do we get to 1-P[(AnB)u(AnB')] from (P[B]+P[B'])-(P[AnB]+P[AnB'])?

The next step suggests:

1.6=2P[A]+1-P[A] and subsequently P[A]=0.6

Also, is there any notable difference between B' (B prime?) and say C or any other variable. Thanks in advance.

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