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Calculadora de probabilidades

Calculate probabilities for two independent events (both, either, exactly one, neither), or for repeated independent trials using the binomial distribution.

O guia abaixo ainda não está disponível em português e é apresentado em inglês. A calculadora está totalmente traduzida.

Como usar esta calculadora

  1. Choose two events or repeated trials.
  2. Enter probabilities as decimals between 0 and 1 (for example 0.25 for 25%).
  3. For repeated trials, enter the number of trials and the number of successes you're interested in.

Fórmula

For independent events, the probability that both happen is the product of their probabilities. Repeated trials follow the binomial distribution.

P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) − P(A)P(B)
P(X = k) = C(n, k) p^k (1 − p)^(n − k)
P(at least once) = 1 − (1 − p)^n

Example

  1. P(A) = 0.5, P(B) = 0.4.
  2. Both: 0.5 × 0.4 = 0.2 (20%). Either: 0.5 + 0.4 − 0.2 = 0.7 (70%).
  3. Neither: 0.5 × 0.6 = 0.3 (30%).

Perguntas frequentes

What are independent events?

Events where one happening doesn't change the probability of the other, such as two separate coin flips. Drawing cards without replacement is not independent.

Why isn't the chance of rolling a six in six rolls 100%?

Each roll is independent. The chance of at least one six is 1 − (5/6)^6 ≈ 66.5%.

How do I convert odds to probability?

Odds of a:b in favour equal a probability of a / (a + b). For example, 3:1 odds = 3/4 = 0.75.