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In a Senate table no senator has an Other affiliation, so no Other senator faces reelection in November 2016. How do those two events relate?
AThey are independent of one another
BThey are equally likely to happen
CThey are mutually exclusive events
DThey are complements of each other
Answer & Solution
Correct answer: C. They are mutually exclusive events
1. No senator carries an Other affiliation, so that event has probability zero.
2. No senator is therefore both an Other and up for reelection in November 2016.
3. The joint probability of the two events is zero, which is exactly the test for mutual exclusivity.
4. They are not complements, since a Democrat facing reelection in 2014 belongs to neither event.
5. They are not equally likely either, because 34 of the 67 senators face reelection in November 2016.
6. Calling them independent misses the point, because independence asks whether one event leaves the chance of the other unchanged, while here the two can never occur together at all.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.5 Venn Diagrams_
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