Probability worksheet using spinners to calculate chances of landing on specific numbers or letters.

Let's solve each question step by step using the two spinners provided in the image.

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

This spinner is divided into 8 equal sections with the following numbers:

- 1 → appears 1 time
- 2 → appears 2 times
- 3 → appears 2 times
- 4 → appears 3 times

So the total number of sections = 8.

We'll use this to calculate probabilities.

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#### 1) What is the probability of the spinner landing on 1 or 3?

- Number of sections with 1 = 1
- Number of sections with 3 = 2
- Total favorable outcomes = 1 + 2 = 3
- Total possible outcomes = 8

$$
P(1 \text{ or } 3) = \frac{3}{8}
$$

✔ Answer: $ \frac{3}{8} $

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#### 2) What is the probability of the spinner not landing on 3?

- Number of sections with 3 = 2
- So, not landing on 3 = 8 - 2 = 6 sections

$$
P(\text{not } 3) = \frac{6}{8} = \frac{3}{4}
$$

✔ Answer: $ \frac{3}{4} $

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#### 3) What is the probability of the spinner not landing on 2?

- Number of sections with 2 = 2
- Not landing on 2 = 8 - 2 = 6 sections

$$
P(\text{not } 2) = \frac{6}{8} = \frac{3}{4}
$$

✔ Answer: $ \frac{3}{4} $

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#### 4) What is the probability of the spinner landing on 1?

- Only 1 section has a 1

$$
P(1) = \frac{1}{8}
$$

✔ Answer: $ \frac{1}{8} $

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#### 5) What is the probability of the spinner landing on 3?

- Two sections have 3

$$
P(3) = \frac{2}{8} = \frac{1}{4}
$$

✔ Answer: $ \frac{1}{4} $

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#### 6) What is the probability of the spinner landing on 4?

- Three sections have 4

$$
P(4) = \frac{3}{8}
$$

✔ Answer: $ \frac{3}{8} $

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#### 7) What is the probability of the spinner not landing on 3 or 4?

- Sections with 3 or 4 = 2 (for 3) + 3 (for 4) = 5
- So not landing on 3 or 4 = 8 - 5 = 3 sections

$$
P(\text{not } 3 \text{ or } 4) = \frac{3}{8}
$$

✔ Answer: $ \frac{3}{8} $

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

This spinner is divided into 6 equal sections:

- A → 1 section
- B → 1 section
- C → 2 sections
- E → 2 sections

Total = 6 sections

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#### 8) Do you have an equal chance of landing on either B or C?

- B: 1 section → $ \frac{1}{6} $
- C: 2 sections → $ \frac{2}{6} = \frac{1}{3} $

Since $ \frac{1}{6} \neq \frac{1}{3} $, the chances are not equal.

✔ Answer: No

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#### 9) What is the probability of the spinner not landing on B or E?

- B: 1 section
- E: 2 sections
- Total B or E = 1 + 2 = 3
- So not B or E = 6 - 3 = 3 sections (A and C)

$$
P(\text{not } B \text{ or } E) = \frac{3}{6} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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#### 10) Do you have an equal chance of landing on either A or C?

- A: 1 section → $ \frac{1}{6} $
- C: 2 sections → $ \frac{2}{6} = \frac{1}{3} $

Not equal.

✔ Answer: No

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#### 11) What is the probability of the spinner landing on A or B?

- A: 1 section
- B: 1 section
- Total = 2

$$
P(A \text{ or } B) = \frac{2}{6} = \frac{1}{3}
$$

✔ Answer: $ \frac{1}{3} $

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#### 12) What is the probability of the spinner not landing on B or C?

- B: 1 section
- C: 2 sections
- B or C = 3 sections
- Not B or C = 6 - 3 = 3 sections (A and E)

$$
P(\text{not } B \text{ or } C) = \frac{3}{6} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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#### 13) Do you have an equal chance of landing on either A or E?

- A: 1 section → $ \frac{1}{6} $
- E: 2 sections → $ \frac{2}{6} = \frac{1}{3} $

Not equal.

✔ Answer: No

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#### 14) What is the probability of the spinner not landing on E?

- E: 2 sections
- Not E = 6 - 2 = 4 sections (A, B, C, C)

$$
P(\text{not } E) = \frac{4}{6} = \frac{2}{3}
$$

✔ Answer: $ \frac{2}{3} $

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | $ \frac{3}{8} $ |
| 2 | $ \frac{3}{4} $ |
| 3 | $ \frac{3}{4} $ |
| 4 | $ \frac{1}{8} $ |
| 5 | $ \frac{1}{4} $ |
| 6 | $ \frac{3}{8} $ |
| 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} $ |

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