Hello, jthomp18!

The problem involves Counting and some simple geometry.

Exactly where is your difficulty?

Consider all of the possibilities of generating a triangle with three diagonals and/or sides of a regular hexagon.

In each case, find the probability that a point inside the hexagon is also inside the triangle. .Explain each solution.

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Case 1: three diagonals.

There are 2 possible triangles.

The area of the triangle is the area of the hexagon.

The probability is

Case 2: two diagonals, one side.

There are 12 possible triangles.

The area of the triangle is the area of the hexagon.

The probability is

Case 3: one diagonal, two sides.

There are 6 possible triangles.

The area of the triangle is the area of the hexagon.

The probability is