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Mutually Exclusive Events

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Mutually Exclusive Events

Study Guide

Key Definition

Mutually exclusive events are those events that cannot occur at the same time. If $A$ and $B$ are mutually exclusive, then $P(A \cap B) = 0$.

Important Notes

Mutually exclusive events cannot happen simultaneously.
The probability of either event occurring: $P(A \cup B) = P(A) + P(B)$
If events are not mutually exclusive: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
Real-life example: Tossing a coin results in heads or tails, not both.
In a single die roll, rolling a 2 and a 5 are mutually exclusive events.

Mathematical Notation

$\cap$ denotes intersection

$\cup$ denotes union

$P(A)$ is the probability of event A

$+$ represents addition

$-$ represents subtraction

Remember to use proper notation when solving problems

Why It Works

The formula $P(A \cup B) = P(A) + P(B)$ applies because mutually exclusive events have no overlap, making $P(A \cap B) = 0$.

Remember

For mutually exclusive events: $P(A \cap B) = 0$ and $P(A \cup B) = P(A) + P(B)$.

Quick Reference

Mutually Exclusive Events:$P(A \cap B) = 0$

Addition Rule:$P(A \cup B) = P(A) + P(B)$

Understanding Mutually Exclusive Events

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Video explanation of this concept

Beginner

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Beginner Explanation

Two events are mutually exclusive when they cannot both happen at the same time, so the probability of their intersection is zero. For example, when rolling a six-sided die, the events “rolling a 2” and “rolling a 5” are mutually exclusive, so P(2 ∩ 5) = 0 and P(2 ∪ 5) = P(2) + P(5) = 1/6 + 1/6 = 1/3.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If $A$ and $B$ are mutually exclusive, what is $P(A \cap B)$?

Practice Quiz

Single Choice Quiz

Intermediate

What is the probability of rolling a 2 or a 5 on a fair six-sided die?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can two events be mutually exclusive and independent at the same time? Explain why or why not.

Challenge Quiz

Single Choice Quiz

Advanced

If $P(A) = 0.3$ and $P(B) = 0.4$ and they are mutually exclusive, what is $P(A \cup B)$?

Recap

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