Probability
Combine two mutually exclusive branches and branch-conditional success rates into total success probability and odds for and against success.
DECISION-TREE ODDS
This calculator evaluates a two-branch chance tree in which branch A or B occurs first and each branch has its own conditional success probability. Program managers and decision analysts can use it to reconcile total success odds, while keeping branch selection and conditional performance as separate evidence.
DECISION-TREE ODDS
Use the two path contributions to identify which branch drives overall success and whether a change to branch selection or branch performance would materially alter the odds.
| Terminal path | Path probability (%) | Payoff | Probability x payoff | Payoff state |
|---|
CURRENT CALCULATION PROCESS
P(S) = P(A)P(S|A) + [1 - P(A)]P(S|B); odds for S = P(S)/[1 - P(S)]
The tree first creates the mutually exclusive A and B branch weights. Each weight is multiplied by its own conditional success or failure rate to produce four terminal path probabilities. The two success paths are added, then probability is converted to odds only after aggregation.
HOW TO USE THIS MODEL
DECISION-TREE ODDS FUNDAMENTALS
MODEL AND FORMULA
The tree first creates the mutually exclusive A and B branch weights. Each weight is multiplied by its own conditional success or failure rate to produce four terminal path probabilities. The two success paths are added, then probability is converted to odds only after aggregation.
DEEPER ANALYSIS
A shift toward the branch with the higher conditional success rate raises overall success even if neither branch improves. Track mix and conditional rates separately to avoid attributing a composition change to better execution.
If branch A counts success at 30 days while branch B counts it at 90 days, the total is not a coherent probability. Align outcome definition, censoring rule, and observation window before combining evidence.
Odds of 1.5 mean 1.5 successes per failure in the long run, corresponding to 60% probability. Reporting 1.5 as "150% likely" is incorrect.
WORKED DECISION CASES
Sixty percent of cases take A and succeed 80% of the time; the remaining 40% take B and succeed 30% of the time. A contributes 48 percentage points and B contributes 12, for 60% total success and odds of 1.5 to 1. The ledger shows that improving B may matter less than expected unless its routing share also changes.
A service team sees total success rise after more cases qualify for its strong A pathway, while both conditional rates stay unchanged. The tree correctly attributes the movement to routing composition; a simple before-and-after total would wrongly imply that every pathway improved.
TECHNICAL LANGUAGE
EVIDENCE AND DATA LINEAGE
Retain the rule that assigns cases to A or B, raw branch counts, branch-specific successes and failures, outcome window, censoring treatment, missing follow-up, and any modeled rather than observed inputs. Confirm that every eligible case appears once and that branch selection is not reconstructed using information available only after the outcome.
LIMITS AND EXCLUSIONS
RELIABLE SOURCES
FREQUENTLY ASKED QUESTIONS
An unweighted average assumes equal branch shares. Total success must weight each conditional rate by the probability of reaching that branch.
No. They preserve a common four-leaf scenario for other tree analyses. This page classifies success by leaf and calculates odds from path probabilities only.
The base model permits an endpoint branch mix. The unused branch then contributes zero path probability, but its conditional input no longer affects the total.
Failure probability becomes zero and odds for success are mathematically infinite. Report the probability and the finite evidence behind it rather than presenting an arbitrary large odds value.
No. Observational branch differences may be caused by selection, eligibility, severity, or timing. Causal claims require an appropriate design beyond this probability reconciliation.
Use an expanded model when branches are not exhaustive, downstream states matter, repeated decisions occur, or consequences depend on more than the four represented leaves.
IMPORTANT NOTE
This page performs exact conditional-probability arithmetic for the entered two-branch structure. It does not establish causal effects, estimate parameter uncertainty, or replace decision governance, validation data, or a more complete event tree when material pathways are omitted.