Probability Calculator
Calculate basic event probability, complementary probability, odds, and the approximate probability of exactly k successes in n binomial trials.
Results
What is it?
Probability measures the likelihood of an event occurring, expressed between 0 (impossible) and 1 (certain). Basic probability = favorable outcomes รท total outcomes. The complement rule states P(not A) = 1 โ P(A). Binomial probability models repeated independent trials where each trial has the same probability of success.
How to use
Enter the number of favorable outcomes and total equally-likely outcomes for basic probability. For binomial analysis, set the number of trials (n) and target successes (k). Note: the Binomial output shows pแต ร (1โp)^(nโk), which is the probability of one specific ordered sequence โ multiply by C(n,k) for the full binomial probability.
Example scenario
Rolling a 6-sided die, probability of rolling a 3: favorable=1, total=6 โ P=16.67%. Odds against = 5:1. In 10 rolls, what is the ordered probability of exactly 3 sixes: (1/6)ยณ ร (5/6)โท โ 0.000558. Multiply by C(10,3)=120 to get the true binomial probability โ 0.0155 (1.55%).
Pro tip
The complement rule is often the fastest path: instead of calculating the probability of getting at least one success in n trials, calculate 1 โ P(zero successes) = 1 โ (1โp)โฟ. For example, the probability of rolling at least one six in 4 rolls = 1 โ (5/6)โด โ 51.8%. Bayes' theorem lets you update probabilities as new evidence arrives: P(A|B) = P(B|A)ยทP(A) / P(B).