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Decoding Probabilities: Unions, Intersections, and Complements
Chapter 1, Problem 1.1-6(choose chapter or problem)
If \(P(A)=0.4, P(B)=0.5\), and \(P(A \cap B)=0.3\), find
(a) \(P(A \cup B)\),
(b) \(P\left(A \cap B^{\prime}\right)\), and
(c) \(P\left(A^{\prime} \cup B^{\prime}\right)\).
Questions & Answers
QUESTION:
If \(P(A)=0.4, P(B)=0.5\), and \(P(A \cap B)=0.3\), find
(a) \(P(A \cup B)\),
(b) \(P\left(A \cap B^{\prime}\right)\), and
(c) \(P\left(A^{\prime} \cup B^{\prime}\right)\).
ANSWER:Step 1 of 3
We have,
P(A) = 0.4,
P(B) = 0.5 and
\(\mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.3\)
We need to find,
\(\mathrm{P}(\mathrm{A} \cup \mathrm{B})\),
\(\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}^{\prime}\right)\) and
\(\mathrm{P}\left(\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}\right)\).
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Decoding Probabilities: Unions, Intersections, and Complements
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Explore the intricacies of calculating probabilities using set theory concepts such as union and intersection. With step-by-step computations, understand how to find the likelihood of events A and B occurring or not occurring together. Witness the application of classic probabilistic formulas.