Compute probabilities for binomial, normal, Poisson, and other distributions.
A probability calculator handles common probability problems: permutations and combinations (counting arrangements), conditional probability, Bayes' theorem, and discrete probability distributions (binomial, Poisson). Essential for combinatorics homework, gambling odds, quality control, and any kind of risk analysis.
The fundamental rule: P(A and B) = P(A) × P(B | A). When events are independent, P(B | A) = P(B). When dependent, conditional probability changes the second factor. Confusing the two is the #1 source of probability errors.
_nP_k = \frac{n!}{(n-k)!} \;;\; _nC_k = \frac{n!}{k!(n-k)!}
Inputs: How many 5-card poker hands are possible from a 52-card deck?
The mistaken belief that past random events affect future ones. After 5 consecutive reds on a roulette wheel, the next spin still has the same 18/37 probability of red — the wheel has no memory. Casinos profit from this fallacy when bettors increase wagers after losses, expecting a "due" win. Independent events stay independent.
Bayes' theorem updates the probability of a hypothesis given new evidence: P(H|E) = P(E|H) × P(H) / P(E). Classic example: a disease has prevalence 1% (P(H)). A test is 95% accurate (P(E|H) = 0.95). If positive, the probability you actually have the disease is only ~16% — counter-intuitive because the false-positive rate (5%) is multiplied by the much larger healthy population. Bayes is the foundation of medical screening, spam filtering, and ML inference.
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