Problem

Amanda has 4 office assistants. If $A$ is the event that at least 3 of them are men and $B$ is the event that at least 3 of them are women, are $A$ and $B$ mutually exclusive? Choose the correct answer below. No Yes

Solution

Step 1 :Define event $A$ as at least 3 of the office assistants are men and event $B$ as at least 3 of them are women.

Step 2 :Mutually exclusive events cannot occur at the same time.

Step 3 :If at least 3 of the office assistants are men (event $A$), then there can be at most 1 woman.

Step 4 :Similarly, if at least 3 of the office assistants are women (event $B$), then there can be at most 1 man.

Step 5 :Therefore, the events $A$ and $B$ cannot occur at the same time, so they are mutually exclusive.

Step 6 :Final Answer: \(\boxed{\text{Yes}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/0tJ6MczqtZ/

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