Probability worksheet featuring two spinners with questions on calculating the likelihood of landing on specific numbers and letters.

Problem Analysis and Solution

The worksheet involves two spinners, and we need to calculate probabilities for each spinner based on the given questions. Let's solve each part step by step.

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#### Spinner 1 (Numbers: 1, 2, 3, 4)

The spinner is divided into 8 equal sections, with the numbers distributed as follows:
- Number 1: 1 section
- Number 2: 2 sections
- Number 3: 1 section
- Number 4: 4 sections

Total sections = 8.

##### Question 1: What is the probability of the spinner landing on 1 or 3?
- Probability of landing on 1: \( \frac{1}{8} \)
- Probability of landing on 3: \( \frac{1}{8} \)
- Combined probability: \( \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \)

Answer: \( \frac{1}{4} \)

##### Question 2: What is the probability of the spinner not landing on 3?
- Probability of landing on 3: \( \frac{1}{8} \)
- Probability of not landing on 3: \( 1 - \frac{1}{8} = \frac{7}{8} \)

Answer: \( \frac{7}{8} \)

##### Question 3: What is the probability of the spinner not landing on 2?
- Probability of landing on 2: \( \frac{2}{8} = \frac{1}{4} \)
- Probability of not landing on 2: \( 1 - \frac{2}{8} = \frac{6}{8} = \frac{3}{4} \)

Answer: \( \frac{3}{4} \)

##### Question 4: What is the probability of the spinner landing on 1?
- Probability of landing on 1: \( \frac{1}{8} \)

Answer: \( \frac{1}{8} \)

##### Question 5: What is the probability of the spinner landing on 3?
- Probability of landing on 3: \( \frac{1}{8} \)

Answer: \( \frac{1}{8} \)

##### Question 6: What is the probability of the spinner landing on 4?
- Probability of landing on 4: \( \frac{4}{8} = \frac{1}{2} \)

Answer: \( \frac{1}{2} \)

##### Question 7: What is the probability of the spinner not landing on 3 or 4?
- Probability of landing on 3: \( \frac{1}{8} \)
- Probability of landing on 4: \( \frac{4}{8} = \frac{1}{2} \)
- Combined probability of landing on 3 or 4: \( \frac{1}{8} + \frac{4}{8} = \frac{5}{8} \)
- Probability of not landing on 3 or 4: \( 1 - \frac{5}{8} = \frac{3}{8} \)

Answer: \( \frac{3}{8} \)

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#### Spinner 2 (Letters: A, B, C, E)

The spinner is divided into 6 equal sections, with the letters distributed as follows:
- Letter A: 1 section
- Letter B: 1 section
- Letter C: 2 sections
- Letter E: 2 sections

Total sections = 6.

##### Question 8: Do you have an equal chance of landing on either B or C?
- Probability of landing on B: \( \frac{1}{6} \)
- Probability of landing on C: \( \frac{2}{6} = \frac{1}{3} \)
- Since \( \frac{1}{6} \neq \frac{1}{3} \), the chances are not equal.

Answer: No

##### Question 9: What is the probability of the spinner not landing on B or E?
- Probability of landing on B: \( \frac{1}{6} \)
- Probability of landing on E: \( \frac{2}{6} = \frac{1}{3} \)
- Combined probability of landing on B or E: \( \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \)
- Probability of not landing on B or E: \( 1 - \frac{3}{6} = \frac{3}{6} = \frac{1}{2} \)

Answer: \( \frac{1}{2} \)

##### Question 10: Do you have an equal chance of landing on either A or C?
- Probability of landing on A: \( \frac{1}{6} \)
- Probability of landing on C: \( \frac{2}{6} = \frac{1}{3} \)
- Since \( \frac{1}{6} \neq \frac{1}{3} \), the chances are not equal.

Answer: No

##### Question 11: What is the probability of the spinner landing on A or B?
- Probability of landing on A: \( \frac{1}{6} \)
- Probability of landing on B: \( \frac{1}{6} \)
- Combined probability: \( \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \)

Answer: \( \frac{1}{3} \)

##### Question 12: What is the probability of the spinner not landing on B or C?
- Probability of landing on B: \( \frac{1}{6} \)
- Probability of landing on C: \( \frac{2}{6} = \frac{1}{3} \)
- Combined probability of landing on B or C: \( \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \)
- Probability of not landing on B or C: \( 1 - \frac{3}{6} = \frac{3}{6} = \frac{1}{2} \)

Answer: \( \frac{1}{2} \)

##### Question 13: Do you have an equal chance of landing on either A or E?
- Probability of landing on A: \( \frac{1}{6} \)
- Probability of landing on E: \( \frac{2}{6} = \frac{1}{3} \)
- Since \( \frac{1}{6} \neq \frac{1}{3} \), the chances are not equal.

Answer: No

##### Question 14: What is the probability of the spinner not landing on E?
- Probability of landing on E: \( \frac{2}{6} = \frac{1}{3} \)
- Probability of not landing on E: \( 1 - \frac{2}{6} = \frac{4}{6} = \frac{2}{3} \)

Answer: \( \frac{2}{3} \)

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Final Answers:

1. \( \frac{1}{4} \)
2. \( \frac{7}{8} \)
3. \( \frac{3}{4} \)
4. \( \frac{1}{8} \)
5. \( \frac{1}{8} \)
6. \( \frac{1}{2} \)
7. \( \frac{3}{8} \)
8. No
9. \( \frac{1}{2} \)
10. No
11. \( \frac{1}{3} \)
12. \( \frac{1}{2} \)
13. No
14. \( \frac{2}{3} \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \frac{1}{4} \\
2. \frac{7}{8} \\
3. \frac{3}{4} \\
4. \frac{1}{8} \\
5. \frac{1}{8} \\
6. \frac{1}{2} \\
7. \frac{3}{8} \\
8. \text{No} \\
9. \frac{1}{2} \\
10. \text{No} \\
11. \frac{1}{3} \\
12. \frac{1}{2} \\
13. \text{No} \\
14. \frac{2}{3}
\end{array}
}
\]