# If we roll a fair number cube, what is the probability of a 5 being rolled, given that we know an odd number has been rolled?

$\frac{1}{3}$
If we throw a die, there is a $\frac{1}{6}$ probability that a 5 will come up. This is done without any other knowledge about the die.
However, we are given a piece of information - that the number is odd. What now is the probability a 5 has been rolled? We know there are only 3 odd numbers on a die (1, 3, 5) and so there are only 3 numbers that the roll could possibly be, meaning the probability of rolling a 5 knowing that the number is odd is $\frac{1}{3}$