You can always use the formula for conditional probabilities:
> P(A|B) = P(AB)/P(B)
> This is the probability of A *given* B.
In this case, A = getting a 1, B = getting an odd number.
> P(AB) is the probability of getting a number that is 1 and odd, which is just the same as getting a 1. P(AB) = P(roll 1) = 1/6
> P(B) is the probability of getting any odd number. Half of the numbers are odd (1,3, and 5), so P(B) = 1/2
P(A|B) = (1/6)/(1/2) = 2/6
> **P(A|B) = 1/3**
This makes sense intuitively too. If you rolled an odd number, that means you know you rolled a 1, 3, or 5. That’s three possible outcomes, all of which are equally likely. Then the probability of each outcome is 1/3.
