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An experiment has outcomes 1 to 12, with A = {1, 2, 3, 4, 5, 6} and B = {6, 7, 8, 9}. Which outcomes lie in neither set?
AThe outcomes 10, 11 and 12
BThe outcome 6 on its own
CThe outcomes 7, 8 and 9
DThe outcomes 1, 2 and 3
Answer & Solution
Correct answer: A. The outcomes 10, 11 and 12
1. The union of A and B covers the outcomes 1 through 9.
2. The outcomes 10, 11 and 12 appear in neither set.
3. On the diagram they sit inside the box but outside both circles, since they are part of the universe without belonging to either event.
4. The outcome 6 lies in both sets at once, so it is the intersection rather than the leftover.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.5 Venn Diagrams_
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