Question

If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade.

Answer 1

We have 13 spades in a standard pack of cards.
Let's take cases.
Case 1: First card -- spade
Our sampling space is 52 cards, it isn't changed because we still haven't drawn anything.

Taken that it's a spade, our sampling space is reduced because it is dependent of our first event.

Case 2: Second card -- spade
Given that we don't replace the card, the second card is dependent of the first card. If we pick up a spade on the first draw, we have 51 cards to choose 12 spades.

(ie 4/17)

Answer 2

There are 13 spades in a standard deck of cards, so if the first one is a spade, there are 12 spades left.

So the chances of getting another one would be 12/52 because there are 52 cards in a standard deck of cards.

Reduced, your answer is 3/13