What is the conditional probability of drawing an ace given the first card is a king?

The conditional probability of drawing an ace given the first card is a king is 4/51.

To understand this, let's break it down. A standard deck of cards has 52 cards, consisting of 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards, including one king and one ace. When you draw the first card and it is a king, you are left with 51 cards in the deck.

Since the first card drawn is a king, there are now 4 aces remaining in the deck of 51 cards. The conditional probability is calculated by considering the number of favourable outcomes (drawing an ace) over the total number of possible outcomes (the remaining cards in the deck).

So, the probability of drawing an ace given that the first card drawn is a king is:
\[ \frac{\text{Number of aces left}}{\text{Total number of remaining cards}} = \frac{4}{51} \]

This fraction represents the likelihood of drawing an ace after a king has already been drawn. It's important to note that the initial draw of the king affects the total number of cards left in the deck, which is why we use 51 as the denominator instead of 52. This is a key concept in conditional probability, where the condition (drawing a king first) changes the sample space (the remaining cards).