https://file.aiquickdraw.com/mathbot/file/1726532957338wzn2uq40.jpg

Let's go through the questions visible in the image and solve them one by one.

### 1. Spinner Questions (Fluency)
The spinner in the image is divided into four sections: 2, 4, 3, 4.

#### a) **List the sample space for the spinner.**
The sample space includes all the possible outcomes when the spinner is spun. Based on the visible numbers, the sample space is:
- \( S = \{2, 4, 3, 4\} \)

#### b) **List the possible outcomes for the spinner.**
The possible outcomes are the distinct numbers on the spinner:
- \( \{2, 3, 4\} \)

#### c) **What is the probability of spinning a 4 on a spin?**
There are two sections on the spinner with the number 4 out of a total of 4 sections.
- Probability of spinning a 4 = \( \frac{2}{4} = \frac{1}{2} \)

#### d) **What is the probability of spinning a number higher than 1?**
All numbers on the spinner (2, 3, 4) are higher than 1, so the probability is 1, or 100%.

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### 2. Coin Toss Experiment (Fluency)
The coin was tossed 10 times, and the results shown are: Head, Tail, Tail, Head, Head, Tail, Head, Tail, Head, Head.

#### a) **List the sample space for the experiment.**
The sample space for a coin toss is:
- \( S = \{\text{Head}, \text{Tail}\} \)

#### b) **How many times did it land on heads and tails?**
- Heads = 6 times
- Tails = 4 times

#### c) **If we continued with the experiment to a total of 100 tosses, what should the results show?**
If the experiment is fair, we expect about 50% heads and 50% tails in the long run (based on probability). So, for 100 tosses, we expect approximately:
- 50 heads
- 50 tails

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### Problem Solving Questions

#### 1. **Complete the spinner using 2 colors (blue and red), so that blue is 3 times more likely to occur than red.**
To achieve this probability distribution, you need to divide the spinner into parts. Since blue is 3 times more likely than red, we need 4 sections in total, where 3 sections will be blue and 1 section will be red.

#### 2. **Complete the spinner using 3 colors (green, blue, black), so that green is 2 times more likely to occur than blue, and black is 3 times more likely to occur than blue.**
This spinner would need to be divided into sections where:
- If blue is \( x \), then green would be \( 2x \) and black would be \( 3x \).
- To make this work, you could divide the spinner into 6 parts: 1 part blue, 2 parts green, and 3 parts black.

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Would you like further details or have any specific questions?

Here are 5 follow-up questions to expand on the concepts:
1. What is the probability of spinning a 3 on the spinner?
2. If the coin toss experiment was repeated 50 times, what would be the expected number of heads?
3. How would you modify the spinner if blue were 4 times more likely than red?
4. What is the probability of getting two tails in a row in the coin toss?
5. Can you design a similar probability problem using a six-sided die?

**Tip**: In probability, always remember that the total number of possible outcomes (sample space) is essential for calculating the likelihood of each event.

Solve the probability questions involving a spinner and a coin toss experiment.

Learn how to solve probability problems involving a spinner and coin tosses. The worksheet covers sample space, experimental probability, and the expected results in repeated trials. Suitable for students in Grades 4-6.

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