Como usar (3 passos)
- Choose Tree (sequential trials) or 2×2 table (A/¬A × B/¬B).
- Enter branch probabilities (tree) or counts/probabilities (table).
- Build the event with AND / OR / NOT and read the highlighted cases + steps.
Tip: For “at least one”, the complement method often uses fewer cases.
Examples
Entradas
Cells are a = A∩B, b = A∩¬B, c = ¬A∩B, d = ¬A∩¬B.
| B | ¬B | |
|---|---|---|
| A | ||
| ¬A |
Display / settings
Teacher notes
- AND (A∩B): one path → multiply branch probabilities.
- OR (A∪B): multiple paths/cells → sum the matching cases (avoid double counting).
- Complement (Ac): P(Ac) = 1 − P(A); great for “at least one”.
Event builder (AND / OR / NOT)
Your selection is the event you want. The tool highlights matching paths/cells and sums their probabilities.
Resultado
Visuals (highlighted)
Tree diagram
Leaf list (accessible)
2×2 table
Como é calculado
Perguntas frequentes
O que é the difference between AND and OR in probability?
AND means both happen (intersection), often computed by multiplying along a tree path. OR means either happens (union), computed by summing matching cases without double counting.
How Devo handle “at least one” questions?
Try the complement: P(at least one) = 1 − P(none). This tool can suggest the opposite event when it uses fewer cases.
Por que the 2×2 table use P(A∪B)=P(A)+P(B)−P(A∩B)?
P(A)+P(B) counts the overlap A∩B twice. Subtracting P(A∩B) removes the double count, and the table makes the overlap cell visible.
What if the branch probabilities in a stage do not sum to 1?
Each stage must sum to 1 because it covers all outcomes at that stage. The tool shows which stage is off and the current sum.