Students can practice calculating theoretical probability with this engaging worksheet featuring various spinner diagrams.

Problem: Calculating Theoretical Probability

The task involves calculating the probabilities of various events for spinners divided into equal sections. Let's solve each problem step by step.

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#### Problem 1:
A spinner is divided into 6 equal sections labeled A, B, C, D, E, and F. Calculate the probabilities of the following events:

1. P(not B): Probability of not landing on B.
2. P(A): Probability of landing on A.
3. P(E and C): Probability of landing on both E and C (simultaneously).
4. P(F or D): Probability of landing on either F or D.

##### Solution:
- Total sections: 6
- Probability of any single section: \( \frac{1}{6} \)

1. P(not B):
- There are 5 sections that are not B (A, C, D, E, F).
- \( P(\text{not B}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{6} \).

2. P(A):
- There is 1 section labeled A.
- \( P(A) = \frac{1}{6} \).

3. P(E and C):
- It is impossible to land on both E and C simultaneously since the spinner can only land on one section at a time.
- \( P(E \text{ and } C) = 0 \).

4. P(F or D):
- There are 2 sections that are either F or D.
- \( P(F \text{ or } D) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{6} = \frac{1}{3} \).

##### Final Answers for Problem 1:
\[
\boxed{\frac{5}{6}, \frac{1}{6}, 0, \frac{1}{3}}
\]

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#### Problem 2:
A spinner is divided into 4 equal sections labeled A, B, C, and D. Calculate the probabilities of the following events:

1. P(not A): Probability of not landing on A.
2. P(B): Probability of landing on B.
3. P(B or C): Probability of landing on either B or C.
4. P(D and C): Probability of landing on both D and C (simultaneously).

##### Solution:
- Total sections: 4
- Probability of any single section: \( \frac{1}{4} \)

1. P(not A):
- There are 3 sections that are not A (B, C, D).
- \( P(\text{not A}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{4} \).

2. P(B):
- There is 1 section labeled B.
- \( P(B) = \frac{1}{4} \).

3. P(B or C):
- There are 2 sections that are either B or C.
- \( P(B \text{ or } C) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{4} = \frac{1}{2} \).

4. P(D and C):
- It is impossible to land on both D and C simultaneously.
- \( P(D \text{ and } C) = 0 \).

##### Final Answers for Problem 2:
\[
\boxed{\frac{3}{4}, \frac{1}{4}, \frac{1}{2}, 0}
\]

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#### Problem 3:
A spinner is divided into 5 equal sections labeled A, B, C, D, and E. Calculate the probabilities of the following events:

1. P(A or C): Probability of landing on either A or C.
2. P(B): Probability of landing on B.
3. P(E and D): Probability of landing on both E and D (simultaneously).
4. P(not D): Probability of not landing on D.

##### Solution:
- Total sections: 5
- Probability of any single section: \( \frac{1}{5} \)

1. P(A or C):
- There are 2 sections that are either A or C.
- \( P(A \text{ or } C) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{5} \).

2. P(B):
- There is 1 section labeled B.
- \( P(B) = \frac{1}{5} \).

3. P(E and D):
- It is impossible to land on both E and D simultaneously.
- \( P(E \text{ and } D) = 0 \).

4. P(not D):
- There are 4 sections that are not D (A, B, C, E).
- \( P(\text{not D}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{5} \).

##### Final Answers for Problem 3:
\[
\boxed{\frac{2}{5}, \frac{1}{5}, 0, \frac{4}{5}}
\]

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#### Problem 4:
The spinner below has 4 equal sections labeled A, A, B, and C. What is the probability of spinning A or B?

##### Solution:
- Total sections: 4
- Sections labeled A: 2
- Sections labeled B: 1
- Sections labeled C: 1

1. P(A or B):
- There are 3 sections that are either A or B (2 A's and 1 B).
- \( P(A \text{ or } B) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{4} \).

##### Final Answer for Problem 4:
\[
\boxed{\frac{3}{4}}
\]

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#### Problem 5:
The spinner below has 5 equal sections labeled A, B, B, A, and B. What is the probability of not spinning A?

##### Solution:
- Total sections: 5
- Sections labeled A: 2
- Sections not labeled A: 3 (all B's)

1. P(not A):
- There are 3 sections that are not A.
- \( P(\text{not A}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{5} \).

##### Final Answer for Problem 5:
\[
\boxed{\frac{3}{5}}
\]

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Final Summary of All Answers:

1. \(\boxed{\frac{5}{6}, \frac{1}{6}, 0, \frac{1}{3}}\)
2. \(\boxed{\frac{3}{4}, \frac{1}{4}, \frac{1}{2}, 0}\)
3. \(\boxed{\frac{2}{5}, \frac{1}{5}, 0, \frac{4}{5}}\)
4. \(\boxed{\frac{3}{4}}\)
5. \(\boxed{\frac{3}{5}}\)