You pick a card at random. Without putting the first card back, you pick a second card at random.

1

2

3

What is the probability of picking an even number and then picking an even number?

*Simplify your answer and write it as a fraction or whole number.*

We are given three cards numbered \(1\), \(2\), and \(3\). The task is to find the probability of picking an even number first, followed by another even number without replacement.

### Step 1: Determine the even numbers.
In this set of three cards, the only even number is \(2\).

### Step 2: First pick.
The probability of picking an even number (which is \(2\)) on the first draw is:
\[
\frac{1}{3}
\]

### Step 3: Second pick.
Since we do not replace the first card, we are left with two cards: \(1\) and \(3\), which are both odd. Therefore, there are no even numbers left for the second pick.

Thus, the probability of picking an even number on the second draw is:
\[
0
\]

### Step 4: Total probability.
The probability of picking an even number and then another even number is the product of the two individual probabilities:
\[
\frac{1}{3} \times 0 = 0
\]

Thus, the probability of picking an even number followed by another even number is **0**.

---

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the probability of picking two odd numbers?
2. What is the probability of picking an odd number followed by an even number?
3. How does the probability change if we replace the first card before drawing again?
4. What is the probability of picking an odd number first and then another odd number?
5. What is the probability of picking two numbers that sum to an odd number?

**Tip:** When calculating probabilities for multiple events, always multiply the probabilities of each event occurring sequentially.

You pick a card at random. Without putting the first card back, you pick a second card at random. What is the probability of picking an even number and then picking an even number?

Explore the probability of picking two even numbers from a set of cards numbered 1, 2, and 3 without replacement. This detailed step-by-step solution covers key concepts such as probability rules and events without replacement. Suitable for students in Grades 6-8.

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