MathIsimple

Conditional Probability

Master conditional probability, the multiplication rule, independence, and Bayes' theorem to solve complex probability problems!

10th Grade
Probability
~60 min
🎮 Interactive Activity: Conditional Probability Calculator

Calculate conditional probabilities!

Problem:

P(A) = 0.4, P(B|A) = 0.6. Find P(A and B)
🎮 Interactive Activity: Bayes Theorem Solver

Use Bayes' theorem to find conditional probabilities!

Problem:

P(A) = 0.3, P(B|A) = 0.8, P(B|not A) = 0.4. Find P(A|B)
1. Introduction to Conditional Probability

What Is Conditional Probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It's written as P(A|B), read as "the probability of A given B."

Key Concept: When we know B has occurred, we restrict our sample space to only outcomes where B is true, then find the probability of A within that restricted space.

Example 1: Basic Conditional Probability

In a deck of 52 cards, what's the probability of drawing an ace given that you've drawn a red card?

Given: Red card drawn (26 red cards)

Red aces: 2 (ace of hearts, ace of diamonds)

P(ace|red): 2/26 = 1/13

Example 2: Real-World Application

If 60% of students pass math and 40% pass both math and science, what's the probability of passing science given they passed math?

Given: P(math) = 0.6, P(math and science) = 0.4

P(science|math): 0.4/0.6 = 2/3 ≈ 0.667

2. Definition and Formula
3. Multiplication Rule
4. Independent Events
5. Bayes' Theorem
6. Tree Diagrams
7. Real-World Applications
8. Problem-Solving Strategies
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
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Correct
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1
What is the formula for conditional probability P(A|B)?
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2
If P(A) = 0.4 and P(B|A) = 0.6, what is P(A and B)?
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3
Two events A and B are independent if:
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4
What is Bayes' theorem used for?
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5
If P(A and B) = 0.3 and P(B) = 0.5, what is P(A|B)?
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6
A test is 95% accurate for disease (2% prevalence). If test is positive, what is P(disease|positive)?
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7
What is the multiplication rule for probability?
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8
If P(A) = 0.3, P(B) = 0.4, and P(A and B) = 0.12, are A and B independent?
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9
What does P(A|B) represent?
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10
In Bayes' theorem, what is P(B|A) called?
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