A die is thrown. Which set of events is exhaustive?

\{1, 2\}, \{3, 4\}, \{5\}

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\{2, 4, 6\}, \{1, 3\}

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\{1, 2\}, \{2, 3, 4\}, \{4, 5, 6\}

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\{1, 3, 5\}, \{2, 3, 5\}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Events are exhaustive when together they cover the whole sample space $\{1, 2, 3, 4, 5, 6\}$ .
$\{1, 2\} \cup \{2, 3, 4\} \cup \{4, 5, 6\}$ is everything; the others miss 6, 5, and 4 and 6.

Worth noting

Exhaustive events may overlap; these share 2 and 4 and are still exhaustive.

Ten questions from Probability, at your own pace.

Explanation