Kenneth S. answered • 05/29/18
Tutor
4.8
(62)
Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
Your use of apostrophes surrounding ∪B is non-standard.
To make sense of this, I rephrase your question--what is P(A∪B) ?
ANSWER: P(A∪B) = P(A) + P(B) - P(A∩B)
and this is not the same as 1-P(AUB).
Kenneth S.
Draw two circles (a Venn diagram with partially overlapping circles A & B, all contained in a rectangle.
Label individual areas as follows.
c: in the area common to the two circles; this represents P(A∩B)
a: in the part of circle A that excludes the above; b in the part of circle B that excludes the above
d: the part within the rectangle excluding a,b,c (outside the "figure 8")
If a,b,c,d are decimal values their sum must be 1.
Now P(A' ) = b+d
P(B') = a + d
P(A' ∪ B') = a+b+d
P(A∪B) =a+b+c
1-P(A∪B) = d
I now see that your original notation (in the original question) made sense, although I would have put a space after the first Union symbol to make it clearer.
Anyway, this new discussion of mine shows why the answer to your question is NO.
Report
05/29/18
Jenny A.
05/29/18