Expected Value of Die until I roll an even number

Question

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 1

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 $\frac13$.