Probability, Combinatorics & Bayesian Calculator
Compute permutations and combinations, evaluate independent & conditional probability events, and solve Bayesian inverse probabilities
e.g., American Roulette wheel slots
Calculated Event Probability P(E)
8.11%
Unlikely Event (< 10%)
Decimal: 0.08108 • Fraction: 3 / 37
Odds Against Winning
34 : 3
Unfavorable to Favorable (11.33 : 1)
Odds in Favor
3 : 34
Favorable to Unfavorable
Complementary Probability P(E’)
91.89%
Probability of event NOT occurring
Expected Value Indicator
1 in 12.33 trials
Average trial recurrence frequency
e.g., 52 playing cards
e.g., 5-card poker hand
Combinations C(n, r) – Order Irrelevant
2,598,960
1 in 2,598,960 chance (Royal Flush / Poker odds)
Permutations P(n, r) – Order Matters
311,875,200
Arrangements where sequence counts
Factorial n!
8.066 × 10⁶⁷
Total full permutation sequences
Combinations with Repetition
3,819,816
Multiset combinations n+r-1 C r
Power Set (2ⁿ Subsets)
4.503 × 10¹⁵
Total possible subset combinations
Medical / Diagnostic Screening Parameters
1.0% base rate in population
True positive test rate (95%)
True negative test rate (90%)
Posterior Probability P(Disease | Positive Test)
8.85%
Base Rate Fallacy Warning
Despite 95% test accuracy, only 8.85% chance of actual disease upon positive test
False Positive Rate P(+ | Healthy)
10.00%
1 – Specificity (Type I error)
Total Positive Test Rate P(+)
10.85%
True positives + False positives
Negative Predictive Value P(Healthy | -)
99.94%
Confidence of negative test result
Likelihood Ratio Positive (LR+)
9.50
Sensitivity ÷ False Positive Rate