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?
Let's look at the problem this way:
If we throw a die, there is a
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