Tree Diagram Visualization

Visualize conditional probabilities with events A and B. Click on intersection probabilities to highlight paths.

P(A) = 0.600

P(B|A) = 0.700

P(B|Aᶜ) = 0.300

Calculated Probabilities

Click on any joint probability to highlight its path through the tree

Joint Probabilities

A ∩ B = P(A) × P(B|A) = 0.4200

A ∩ Bᶜ = P(A) × P(Bᶜ|A) = 0.1800

Aᶜ ∩ B = P(Aᶜ) × P(B|Aᶜ) = 0.1200

Aᶜ ∩ Bᶜ = P(Aᶜ) × P(Bᶜ|Aᶜ) = 0.2800

Marginal Probabilities

P(A) = 0.6000

P(Aᶜ) = 0.4000

P(B) = P(A∩B) + P(Aᶜ∩B) = 0.5400

P(Bᶜ) = 0.4600

Conditional: Given A

P(B|A) = 0.7000

P(Bᶜ|A) = 0.3000

Conditional: Given Aᶜ

P(B|Aᶜ) = 0.3000

P(Bᶜ|Aᶜ) = 0.7000

Bayes Theorem

P(A|B) = P(B|A) × P(A) / P(B) = 0.7778

P(Aᶜ|B) = P(B|Aᶜ) × P(Aᶜ) / P(B) = 0.2222

How to use: Adjust the sliders to change probabilities. Click on any joint probability block to highlight its path through the tree.

How Tree Diagrams Work

Conditional Probabilities in Trees

Practical Applications

Understanding Conditional Probability with Tree Diagrams

Tree diagrams show sequential events as branching paths. Each branch represents a possible outcome, with conditional probabilities displayed along the paths. This visualization is perfect for understanding multi-stage probability problems.

How Tree Diagrams Work

Tree diagrams display events in chronological order from left to right. Each branch splits into possible outcomes, with probabilities labeled on each path. The final probability of any outcome is found by multiplying along its path.

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Conditional Probabilities in Trees

Each level of branches represents conditional probabilities - the probability of an event given the previous outcome. This makes tree diagrams ideal for understanding P(A|B) notation and sequential decision-making.

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Practical Applications

Tree diagrams excel at modeling sequential decisions, medical testing scenarios, quality control processes, and any situation where outcomes depend on previous events.

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