Chapter 32

Concept Explanation:

The addition rule in probability is used when determining the probability that either one of two events occurs. The two versions of the rule are as follows:

1. For Mutually Exclusive Events (events that cannot happen at the same time):

For Non-Mutually Exclusive Events (events that can happen at the same time):

Common Mistakes:

1. Forgetting to Subtract Overlap: When dealing with non-mutually exclusive events, students often forget to subtract .
2. Incorrect Interpretation of “Or”: The word “or” in probability doesn’t always imply mutually exclusive; check if events can overlap.

Helpful Tips:

• Venn Diagrams: Drawing Venn diagrams can help visualize mutually exclusive and non-mutually exclusive events.
• Practice Identifying Event Types: Work on examples to distinguish between mutually and non-mutually exclusive events.

Hard Questions:

Q1: If and , and and are mutually exclusive, find .

Step-by-Step Solution:

1. Since the events are mutually exclusive:

Answer:

• The result is .

Q2: If , , and , find .

Step-by-Step Solution:

1. Since the events are not mutually exclusive, apply the general addition rule:

Answer:

• The result is .

Q3: If , , and the events are mutually exclusive, find .

Step-by-Step Solution:

1. Since the events are mutually exclusive:

Answer:

• The result is .

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