Let's analyze the question from the uploaded image:

Problem

You are picking cards randomly (from numbers 1, 2, 3, 4), replacing them after each pick, and then picking again. The goal is to calculate the probability of picking a number less than 4 first, followed by picking a prime number.

Step 1: First Event - Picking a number less than 4

The numbers less than 4 are 1, 2, 3. There are 3 favorable outcomes out of 4 possible outcomes.

$P(\text{number less than 4}) = \frac{3}{4}$

Step 2: Second Event - Picking a prime number

The prime numbers in this set are 2 and 3. There are 2 favorable outcomes out of 4 possible outcomes.

$P(\text{prime number}) = \frac{2}{4} = \frac{1}{2}$

Step 3: Combined Probability

The events are independent because the card is replaced after each pick. The combined probability is the product of the probabilities of the two events:

$P(\text{number less than 4, then prime}) = P(\text{number less than 4}) \cdot P(\text{prime number})$

Substitute the values:

$P = \frac{3}{4} \cdot \frac{1}{2} = \frac{3}{8}$

Step 4: Convert to Decimal

$\frac{3}{8} = 0.375$

Final Answer:

The probability is:

$\boxed{0.375}$

Would you like further details or explanations? Let me know!

Related Questions:

1. What is the probability of picking a number greater than 2 followed by a prime number?
2. How would the probability change if the cards were not replaced after picking?
3. What is the probability of picking two prime numbers consecutively?
4. What is the probability of picking an even number followed by a number less than 3?
5. If another card labeled "5" was added, how would this affect the probability?

Tip:

When dealing with probabilities, always ensure you carefully consider whether the events are independent or dependent, as this affects the calculations!