To determine the probability $P(3)$ when picking a random card, follow these steps:

1. Understand the problem:

   • We want to find the probability of selecting a card that represents the outcome "3 siblings."
   • The frequency of students with 3 siblings is 9.

2. Calculate the total number of students surveyed:

   • Total number of students = $6$ (with 1 sibling) + $12$ (with 2 siblings) + $9$ (with 3 siblings) + $3$ (with 4 or more siblings) = $30$ students.

3. Calculate the probability $P(3)$:

   • Probability $P(3) = \frac{\text{Number of students with 3 siblings}}{\text{Total number of students}} = \frac{9}{30}$.

4. Simplify the probability:

   • $\frac{9}{30} = \frac{3}{10} = 0.3 = 30\%$.

So, the probability $P(3)$ is 30%.

Would you like further details or have any other questions?

Here are some related questions:

1. What is the probability of selecting a card that represents "4 or more" siblings?
2. How would the probability change if the number of students with 3 siblings increased by 3?
3. What is the probability $P(1)$ when picking a random card?
4. What is the combined probability of selecting a card that represents 2 or 3 siblings?
5. If two cards are drawn, what is the probability that both cards represent "2 siblings"?
6. How would the probability $P(3)$ change if only 20 students were surveyed?
7. What is the probability of picking a card that represents 1 or 2 siblings?
8. How does the distribution of sibling numbers affect the overall probabilities?

Tip: When working with probabilities, ensure that all outcomes are accounted for in the total when calculating the probability of a specific event.