# Given you have rolled one die and it is a 3, what is the probability the next two dice rolled will be two additional 3’s?

Sep 3, 2017

$\frac{1}{36}$

#### Explanation:

The outcome when a die is rolled is independent of any rolls before.
There are always six numbers - you cannot 'use up' any of the numbers.

The probability of throwing any number on a die is $\frac{1}{6}$

$P \left(3 , 3\right) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$

The probability of throwing three consecutive threes is:

$P \left(3 , 3 , 3\right) = \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} = \frac{1}{216}$