Two cards are drawn at random from a pack without replacement. What is the probability that the first is an Ace but the second is not an Ace?

To solve this problem, we need to calculate the probability of two specific events happening in sequence:

1. **First Event:** Drawing an Ace from the deck.
2. **Second Event:** Drawing a non-Ace after the Ace has been drawn, with no replacement.

### Total Number of Cards:
A standard deck of cards contains 52 cards in total.

### Step-by-Step Calculation:

1. **Probability of drawing an Ace first:**
   - There are 4 Aces in the deck.
   - The probability of drawing an Ace first is:
   \[
   \frac{4}{52} = \frac{1}{13}
   \]

2. **Probability of drawing a non-Ace second, after an Ace has been drawn:**
   - After one Ace is drawn, 51 cards remain, and 48 of these are non-Aces.
   - The probability of drawing a non-Ace second is:
   \[
   \frac{48}{51}
   \]

3. **Combined Probability:**
   - Since these two events are sequential and dependent, we multiply the probabilities of each event:
   \[
   \frac{1}{13} \times \frac{48}{51} = \frac{48}{663}
   \]

### Final Answer:
The probability that the first card is an Ace and the second card is not an Ace is:
\[
\frac{48}{663} \approx 0.0724
\]

Would you like any more details or have any other questions?

**Related Questions:**
1. What is the probability of drawing two Aces in succession?
2. What is the probability that both cards drawn are face cards?
3. What is the probability of drawing one red card and one black card in two draws?
4. How does the probability change if the cards are drawn with replacement?
5. What is the probability that neither card drawn is an Ace?

**Tip:** When working with probabilities in card problems, consider the order of events and whether or not replacement occurs, as these factors significantly impact the outcome.

Learn how to calculate the probability of drawing an Ace first and a non-Ace second from a deck of cards without replacement. This problem involves understanding basic probability concepts and sequential events in probability theory. Suitable for high school students.

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