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A die is thrown. Let A be the event "the number is a multiple of 3", and let B be the event "the…

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A die is thrown. Let $A$ be the event "the number is a multiple of $3$ ", and let $B$ be the event "the number is a power of $2$ ", counting $1$ as a power of $2$ . Write both events as sets. Find $n(A \cap B)$ , then $n(A \cup B)$ , and then the number of outcomes that belong to neither event. Decide whether $A$ and $B$ are mutually exclusive, and whether they are exhaustive.

Need a reminder? The key ideaShow

An event is a subset of $S$ . It is simple with one outcome, compound with more. Events $A$ and $B$ are mutually exclusive when $A \cap B = \varnothing$ and exhaustive when $A \cup B = S$ .

The worked solution

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