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.

(In reply to Solution (Full) by tomarken)

Man, you guys are quick.

For my solution, my equations look identical to tomarken's, with the exception of equation 1.  I used the first statement, yielding:

(1) a + 2b + 3c + 4d +5e +6f = 3.5

This (of course) yielded the same solution, "confirmed" by the fact that all 6 probabilities summed to 1.

Posted by Rollercoaster on 2006-04-24 14:11:27