I have an unfair six sided die with the following known characteristics:

1) The expected value is the same as for a fair die;
2) The probability of rolling either 1 or 2 or 5 is the same as the probability of rolling either 4 or 6;
3) The probability of rolling either a 2 or 3 is 1/2;
4) If the die is rolled twice in a row, the probability of getting 6 both times is the same as getting a 2 and then a 5;
5) The probability of rolling a 4 is ten times that of rolling a 1;
6) The probability of rolling a 6 is twice that of rolling a 5.

What is the probability of each side? This can and should be solved by hand.

Side  Probability
-----------------
  1     0.025
  2     0.300
  3     0.200
  4     0.250
  5     0.075
  6     0.150
       ------
        1.000     

The expected value is 3.5 (same as a normal die).

Posted by tomarken on 2006-04-24 13:25:22