 Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is an ace, given that the first card is an ace?

This problem involves conditional probability. We are asked to find the probability that the second card drawn is an ace, given that the first card is also an ace.

### Problem Breakdown:
- A deck contains 52 cards, with 4 aces.
- The event we are interested in is: The second card is an ace, given that the first card is an ace.

This is a conditional probability problem, where we are asked to find \( P(\text{second ace} \mid \text{first ace}) \).

### Solution:
Given that the first card drawn is an ace, there are now:
- 51 cards left in the deck,
- 3 aces remaining in the deck.

The probability of drawing an ace on the second draw, after having drawn one ace already, is simply the ratio of the number of remaining aces to the number of remaining cards:

\[
P(\text{second ace} \mid \text{first ace}) = \frac{3}{51}
\]

Simplifying the fraction:

\[
P(\text{second ace} \mid \text{first ace}) = \frac{1}{17}
\]

Thus, the probability that the second card is an ace given that the first card is an ace is \( \frac{1}{17} \).

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Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. What is the probability of drawing two aces consecutively from a deck?
2. How does the probability change if we replace the first card before drawing the second?
3. What is the probability of drawing two non-ace cards consecutively?
4. What is the probability that at least one ace is drawn in two consecutive draws?
5. How does the probability change if three cards are drawn without replacement?

**Tip:** In problems involving conditional probability, always consider how the total number of favorable outcomes and possible outcomes changes after each event.

Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is an ace, given that the first card is an ace?

Understand how to calculate the conditional probability of drawing two aces consecutively from a deck of 52 cards without replacement. This problem demonstrates key probability concepts and the conditional probability formula, suitable for students in Grades 10-12.

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