What is a Biased Die?

Date: 03/01/2002 at 15:06:04
From: Rehan Basim
Subject: Probability

What is a biased die, and how do we find the probability when the dice 
are biased? Would you please give an example? I would be grateful to 
you.

Date: 03/03/2002 at 23:56:32
From: Doctor Twe
Subject: Re: Probability

Hi Rehan - thanks for writing to Dr. Math.

A biased die is the opposite of a fair die. On a fair die, every 
number has an equal chance of being rolled (1/6 on a cubic 6-sided 
die). On a biased die, some numbers are more likely to be rolled than 
others. This may be due to the die's shape - shaving some edges, for 
example, or having weights inside the die, or other means of "fixing" 
it.

For example, a biased die might have the following probabilities:

     No.   Prob
     ---   ----
      1    1/12 =  1/12
      2    1/12 =  1/12
      3    1/12 =  1/12
      4    1/6  =  2/12
      5    1/4  =  3/12
      6    1/3  =  4/12
                  -----
                  12/12

Notice that the sum of all the probabilities must still equal 1.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.com/dr.math/