Binomial and Poisson Distributions

Binomial and Poisson Distributions Calculator

MathCrave probability solver helps you understand and solve problems related to two of the most important discrete probability distributions. Whether you're calculating the probability of a specific number of successes in a fixed number of trials (Binomial) or the number of events in a fixed interval of time or space (Poisson), this tool provides accurate results and clear explanations.

Binomial Distribution Calculator

Calculate probabilities for binomial experiments. Input the number of trials, probability of success, and the number of successes to get a complete solution.

Poisson Distribution Calculator

Solve for the probability of a given number of events occurring in a fixed interval. Input the average rate of occurrence and the number of events to find the probability.

For an interactive experience solving probability distributions, use MathCrave AI

Binomial Distribution

Binomial Distribution Calculator

Trials (n):

Probability (p):

Successes (k):

Poisson Distribution

Poisson Distribution Calculator

Average rate ($\lambda$):

Events (k):

The binomial distribution describes the number of successes ($k$) in a fixed number of independent trials ($n$), each with a success probability $p$.

$$ P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} $$

The Poisson distribution expresses the probability of a number of events ($k$) occurring in a fixed interval, given an average rate $\lambda$.

$$ P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!} $$

Arithmetic Progression (AP)

Find $n^{th}$ Term ($a_n$) of an AP

$a$ (First Term):

$d$ (Common Diff.):

$n$ (Term Number):

Geometric Progression (GP)

Find $n^{th}$ Term ($a_n$) of a GP

$a$ (First Term):

$r$ (Common Ratio):

$n$ (Term Number):