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Addition Rule in Probability

Master the addition rule in probability with interactive lessons and practice problems! Designed for students aged 10-16 years.

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Addition Rule in Probability

Study Guide

Key Definition

The Addition Rule in Probability states that the probability of either one of two events occurring is given by: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Important Notes

$P(A \cup B)$ is the probability of event A or event B occurring.
$P(A \cap B)$ is the probability of both events A and B occurring.
If events A and B are mutually exclusive, $P(A \cap B) = 0$.
In this case, the Addition Rule simplifies to $P(A \cup B) = P(A) + P(B)$.

Mathematical Notation

$\cup$ indicates the union of two events i.e., either one or both events occur.

$\cap$ indicates the intersection of two events i.e., both events occur.

Remember to use proper notation when solving problems.

Why It Works

The Addition Rule works due to the principle of inclusion and exclusion. We add the probabilities of individual events but subtract the probability of both events occurring to avoid double-counting. Refer to the Venn diagram (see assets/venn-diagram.png) for a visual explanation.

Remember

Always check if the events are mutually exclusive. If they are, the Addition Rule simplifies.

Quick Reference

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

Understanding Addition Rule in Probability

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Using a Venn diagram helps: to find the probability of A or B, add their individual probabilities and subtract the overlap so it’s not counted twice (see assets/venn-diagram.png).

Practice Problems

Test your understanding with practice problems

Real-World Problem

Question Exercise

Intermediate

Card Game

You take out a single card from a regular pack of cards. What is the probability that the card is either an ace or a spade? Refer to the Venn diagram if needed.

Think About It

Thinking Exercise

Beginner

Think About This

What is the probability of rolling a die and getting either a 2 or a 3? Refer to the Venn diagram if needed.

Recap

Watch & Learn

Review key concepts and takeaways