December 2010
Problem of the Month

Double Sixes

If you roll a pair of dice, the probability of getting double sixes is 1/36 or 0.028.

How many times do you need to throw a pair of dice so that the chances of getting double sixes is more than 0.50 or 50%?

Solution to the Problem:

The answer is 25.

Here is a table showing the probability of getting double sixes for various throws of the dice:



So, it would take 25 throws until the probability of getting double sixes is more then 50% or 0.50.

The chance of getting double sixes in two throws is 1 minus the probability of no double sixes in two throws, or 1 - (35/36 x 35/36).

The chance of getting double sixes in three throws is 1 minus the probability of no double sixes in three throws, or 1 - (35/36 x 35/36 x 35/36).

This is very similar to the Birthday Problem.

Correctly solved by no one.

This is the first time in several years that a problem has gone unsolved!   But it was a difficult problem.   Check out the birthday problem above, which is similar and was always a favorite of mine when I taught probability.

Send any comments or questions to: David Pleacher