https://file.aiquickdraw.com/mathbot/file/1726349039948br701iyd.jpg

Let's analyze the image and solve the problems:

### Question 1:
"Fill in the blank. The ______ is the collection of all the sample points in an experiment."

Options:
- A) event
- B) Venn diagram (chosen)
- C) union
- D) sample space

**Correct Answer:** D) sample space

**Explanation:** The collection of all possible outcomes (sample points) of an experiment is known as the *sample space*. A *Venn diagram* is a visual representation of relationships between different sets, while an *event* is any subset of the sample space. A *union* refers to the combined elements of two or more sets.

### Question 2:
A table is provided showing political affiliation and types of jobs for workers. The goal is to find the probability that a randomly selected worker is *not* an Independent.

The table breakdown:
- **White Collar**: 
  - Republican: 17%
  - Democrat: 18%
  - Independent: 16%
- **Blue Collar**: 
  - Republican: 10%
  - Democrat: 9%
  - Independent: 30%

The problem asks for the probability that the worker is not an Independent.

**Step-by-step Calculation:**
1. Total workers across all affiliations:
   - White Collar: \(17\% + 18\% + 16\% = 51\%\)
   - Blue Collar: \(10\% + 9\% + 30\% = 49\%\)

2. Total percentage of Independents:
   - \(16\%\) (White Collar) + \(30\%\) (Blue Collar) = \(46\%\)

3. The probability of not being Independent is \(100\% - 46\% = 54\%\).

**Correct Answer:** D) 0.54

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Would you like any more details or have any questions? Here are five related questions for practice:

1. What is the difference between an event and a sample space in probability?
2. How do you calculate the probability of the union of two events?
3. What is the probability of being a Blue Collar worker and a Democrat in this table?
4. How does a Venn diagram help visualize sample spaces and events?
5. If the data were updated, how would you handle the new probabilities?

**Tip:** Always ensure you consider the complement (opposite event) when calculating "not" probabilities, as in this example with "not an Independent."

Fill in the blank. The ______ is the collection of all the sample points in an experiment.
The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Find the probability the worker is not an Independent.

Learn how to solve a probability problem based on workers' political affiliations and job types in a state. This problem covers key concepts like sample space and complementary events, with step-by-step calculations. Suitable for Grades 9-12.

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