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

3
4
5

What is the probability of picking a 3 and then picking a 4?

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

You are picking cards without replacement, so we need to calculate the probability step by step:

### Step 1: Probability of picking a 3 first
Initially, there are 3 cards (3, 4, and 5). The probability of picking a 3 is:

\[
P(\text{3 first}) = \frac{1}{3}
\]

### Step 2: Probability of picking a 4 after picking a 3
After picking the first card (which is a 3), there are only 2 cards left (4 and 5). The probability of picking a 4 now is:

\[
P(\text{4 second}) = \frac{1}{2}
\]

### Step 3: Combined probability
To find the overall probability of picking a 3 and then picking a 4, we multiply the two probabilities:

\[
P(\text{3 then 4}) = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}
\]

So, the probability of picking a 3 and then a 4 is:

\[
\boxed{\frac{1}{6}}
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What is the probability of picking a 4 and then a 5?
2. How does the probability change if you pick with replacement?
3. What is the probability of picking a 5 and then a 3?
4. What is the probability of picking two cards that are not the same?
5. How would the probability change if you had more cards, say 4 or 5 cards?

**Tip:** When calculating probabilities without replacement, the number of choices decreases as you remove items from the pool!

You pick a card at random. Without putting the first card back, you pick a second card at random. 3 4 5 What is the probability of picking a 3 and then picking a 4? Simplify your answer and write it as a fraction or whole number.

Learn how to calculate the probability of picking a 3 and then a 4 from a set of three cards (3, 4, 5) without replacement. This problem demonstrates key concepts in probability, including dependent events and the multiplication rule. Suitable for students in Grades 6-8.

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