How to calculate conditional probabilities? E.g, say we roll a fair standard six sided die, what is the probability we rolled a 2, given that the roll is even?

Brief overiew of the answer: Since the roll is even, we either rolled a 2, a 4 or a 6, all with equal probabilities. Therefore, the probability we rolled a 2 is equal to 1/3.Formal answer: We write P(2|E) to represent the probability of rolling a 2 given the roll is even, P(2) and P(E) to represent rolling a 2 and rolling an even number respectively. Since we're rolling a fair six sided die, we have P(2) = 1/6, and P(E) = 1/2.Using the formula for conditional probability, we have P(2|E) = P(2 ∩ E)/P(E) = (1/6) / (1/2) = 1/3, where we used the fact that the probability of rolling a 2 and an even number is equal to probability of rolling a 2, since 2 is even.