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Calculate P(A u B) given P(A), P(B) and intersection.
", "licence": "None specified"}, "statement": "Given that
\\[ P(\\var{LIST[1]}) = \\var{pa} \\\\
P(\\var{LIST[2]}) = \\var{pb} \\\\
P(\\var{LIST[1]} \\cap \\var{LIST[2]}) = \\var{inter} \\]
We need to use the general form of the Addition Law of Probability. This law always holds, regardless of whether the variables are independent or mutually exclusive.
The law is:
\\[P(A \\cup B) = P(A) + P(B) - P(A \\cap B)\\]
Substituting in the values we are given:
\\[ \\begin{split}
P(\\var{LIST[1]} \\cup \\var{LIST[2]}) &\\,= \\var{pa} + \\var{pb} - \\var{inter} \\\\ &\\,= \\var{union}
\\end{split} \\]
Calculate $P(\\var{LIST[1]} \\cup \\var{LIST[2]})$
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