probability - Expected Value of Die until I roll an even number

I roll a standard die repeatedly until I roll an even number. What is the probability that the last number rolled is $2$?

The probability of rolling an even number is $\frac12$ but how would you work out what the probability that number is? Would it be the intersection of the two events?

Answer

By the principle of indifference, every even number is equally likely to be the last number rolled. Since a standard die has $6$ sides, there are $3$ even numbers, and their equal probabilities must add up to $1$, so each of them must be $\frac13$.