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For each of the following, state whether the events created are mutually exclusive and collectively exhaustive.


  1. Registered voters in the United States were asked whether they are registered as Republicans or Democrats
  2. Each respondent was classified by the type of car he or she drives: Sedan, SUV, American, European, Asian, or none.
  3. People were asked, ‘’Do you currently live in (a) an apartment or (b) a house?
  4. A product was classified as defective or not defective.
in Data Science by Diamond (50,996 points) | 636 views

1 Answer

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i: Mutually exclusive, as they cannot vote for more than one party. Not collectively exhaustive, as there are other parties they could have voted for.

ii: Not mutually exclusive. People can own more than one car. Just not more than one car can be driven at once. Also not collectively exhaustive. Cars are manufactured in other areas too.

iii. Mutually exclusive, and Not collectively exhaustive. You cannot live in a house and an apartment at the same time, but there are other places to live in.

iv. Mutually exclusive and Collectively exhaustive. It can only be one of the two, and it must be either one. There are no other options
by Wooden (560 points)

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