My problem is as follows: Suppose you draw a card from a 52-card deck and see that the card is a spade. You then draw another card without replacement. What is the probability that the next card is an ace?
I tried solving this question using conditional probability, but the issue is that the Spade that I initially drew could have also been an Ace. Here are the events that I defined:
A = Draw an ace
B = Draw a spade
$P(A | B) = P(A \cap B) / P(B)$
I'm confused how to calculate the intersection in the numerator. Thanks for your help!