Probability for Correctly Guessing a Random Color

Date: 11/16/95 at 20:8:39
From: Anonymous
Subject: probability

Hello Dr. Math.  I have a question.  I am thinking of one color.  There 
are six choices for that color.  Someone guessed my color correctly.  
After that she said, "Let me try to guess again."  She guessed correctly 
the second time and did this again, and again, and again, and again.  
What is the probability of this happening-- that someone could guess 
correctly in a row?  Thank you.

Date: 11/19/95 at 16:14:13
From: Doctor Ethan
Subject: Re: probability

Neat question.

Well the probability depends on how many times in a row your friend
guessed correctly.

For each guess there are six possibilities, so your friend has a 1/6 
chance of guessing right.

So to guess two times in a row right your friend has a 1/6 * 1/6 = 1/36 
chance of being right.  Now still at each guess, the chance is 1/6.

But to make a string of 12 right guesses the odds are 1/6 times itself 12 
times.

Does that help?

-Doctor Ethan,  The Geometry Forum