Unbeatable Dice

The Problem : 

The six faces on four non-standard dice A, B, C, D carry the following numbers of pips:

A: 3, 3, 3, 3, 3, 3

B: 4, 4, 4, 4, 0, 0

C: 5, 5, 5, 1, 1, 1

D: 6, 6, 2, 2, 2, 2

Two players each choose one die, and throw to see who gains the higher score.

If player 1 chooses A and then player 2 chooses B, what is the probability that player 2 wins?

Show that, if player 2 chooses a die after player 1, then player 2 can always be sure of the same probability of winning.

Open the File as a Word Document

 

Send site mail to admin@1000problems.org  or personal comments direct to sdakeyne@psc.ac.uk with questions or comments about this web site.
Last modified: June 18, 2007