Question

question::
three of six vertices of a regular hexagon are chosen at random. the probability that the triangle formed by these vertices is equilateral is??

Answer 1

@mathmale

Answer 2

@satellite73

Answer 3

@whpalmer4

Answer 4

Let's just look at a picture. If we're picking sides at random, what's the probability of our first choice falling on a corner that can make an equilateral triangle? It's 100%, since it's our first choice and any of the 6 can do that for us.

What about the next choice?

Answer 5

Now you can see after we have randomly chosen one corner, our next choice can only be one of the two places shown. And so we have a 2/5 probability of picking this, would you agree? Now after that, what will be our probability of picking the final corner?