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!