# Triangles - Probability

• Oct 3rd 2012, 04:46 PM
jthomp18
Triangles - Probability
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.

to see the picture on this one .. you must click on this link: InterMath

Can anyone help with this problem?
• Oct 3rd 2012, 06:40 PM
Soroban
Re: Triangles - Probability
Hello, jthomp18!

The problem involves Counting and some simple geometry.

Quote:

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.

To see the picture on this one .. you must click on this link: InterMath

Case 1: three diagonals.

There are 2 possible triangles.
The area of the triangle is $\tfrac{1}{2}$ the area of the hexagon.
The probability is $\tfrac{1}{2}.$

Case 2: two diagonals, one side.

There are 12 possible triangles.
The area of the triangle is $\tfrac{1}{3}$ the area of the hexagon.
The probability is $\tfrac{1}{3}.$

Case 3: one diagonal, two sides.

There are 6 possible triangles.
The area of the triangle is $\tfrac{1}{6}$ the area of the hexagon.
The probability is $\tfrac{1}{6}.$