Thirty students were surveyed about the number of siblings they have. Their results were recorded and placed on a card face down.



OutcomeFrequency

1

6

2

12

3

9

4 or more

3


Determine P(3) when picking a random card.

 10% 30% 70% 80%

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.

Learn how to calculate the probability P(3) when picking a random card representing the number of siblings from survey data. This problem involves understanding frequency distributions and calculating probabilities based on surveyed results. Suitable for students in Grades 7-9.

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