Weighted Probability Trees and Total Probability

This page explores the use of weighted probability trees and introduces the concept of total probability.

Weighted probability trees are powerful tools for visualizing and calculating probabilities in multi-step experiments:

Example: In an arbre pondéré - exercice corrigé, each branch represents a possible outcome, with the probability of that outcome written on the branch.

The general structure of a weighted probability tree includes:

• Root node representing the starting point
• Branches representing possible outcomes at each stage
• Probabilities assigned to each branch

Highlight: To calculate the probability of a specific path through the tree, multiply the probabilities along that path.

Key formulas for using weighted probability trees include:

• P(A∩B) = P(A) × P(B|A)
• P(A∩B̄) = P(A) × P(B̄|A)

Definition: The probabilité totale formule is used when the sample space is partitioned into mutually exclusive events.

If events A₁, A₂, ..., An form a partition of the sample space, then for any event B: P(B) = P(B∩A₁) + P(B∩A₂) + ... + P(B∩An)

Vocabulary: Arbre de probabilité en ligne refers to online tools or software that can help create and analyze probability trees digitally.

Highlight: Weighted probability trees are particularly useful for solving complex probability problems involving multiple steps or conditional probabilities.