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. |