Two events that cannot happen at the same time are said to be mutually exclusive.
Not mutually exclusive, see solution.
Practice makes perfect
We are asked whether the events of choosing a triangle that is equilateral and choosing a triangle that is equiangular are mutually exclusive. First, let's recall the definition of mutually exclusive events.
Two events that cannot happen at the same time are said to be mutually exclusive.
Now, let's suppose that we are choosing from the following triangles.
Recall that every equiangular triangle is also equilateral. Therefore, if we choose the first figure, an equiangular triangle, we are choosing a triangle that is equiangular and equilateral at the same time.
This means that the events of choosing a triangle that is equilateral and choosing a triangle that is equiangular can happen at the same time. Thus, the events are not mutually exclusive.
