Probability Tree Calculator
Compute compound event probabilities for a two-stage experiment using multiplication rule.
Inputs
P(A and B)
0.420000
P(A and not B)
0.180000
P(not A and B)
0.120000
P(not A and not B)
0.280000
P(B) total
0.540000
Step by step
Values used
P(Stage 1 outcome A) = 0.6000; P(Stage 2 outcome B | Stage 1 = A) = 0.7000; P(Stage 2 outcome B | Stage 1 = not A) = 0.3000
Multiplication Rule
P(A and B) = P(A) × P(B|A)
Total Probability
P(B) = P(A)×P(B|A) + P(not A)×P(B|not A)
P(A and B)
= 0.420000
P(A and not B)
= 0.180000
P(not A and B)
= 0.120000
P(not A and not B)
= 0.280000
P(B) total
= 0.540000
How it works
A probability tree represents sequential events as branches. Each path probability is the product of probabilities along its branches (multiplication rule). The total probability of any second-stage outcome is the sum across all paths reaching it (law of total probability).
Formulas
Multiplication Rule
P(A and B) = P(A) × P(B|A)
- P(A)
- First stage probability
- P(B|A)
- Second stage conditional probability
Total Probability
P(B) = P(A)×P(B|A) + P(not A)×P(B|not A)
- P(B)
- Overall probability of B
Frequently Asked Questions
What is the multiplication rule?
For sequential events, P(A and B) = P(A) × P(B|A). You multiply along the branches of the tree.
How do I find the total probability of a second-stage outcome?
Sum the probabilities of all paths that end in that outcome. This is the law of total probability.