molbiotools

Useful links Send feedback! User guide
×

# Molbiotools is a collection of free online apps:

 DNA Sequence Tools Text and Data Tools Calculators

This site uses cookies. By proceeding, you agree to our privacy policy, including the use of cookies.

Privacy Policy: Third party vendors, including Google, use cookies to serve ads based on a user's prior visits to this website or other websites. Google's use of advertising cookies enables it and its partners to serve ads to site visitors based on their visits to this site and/or other sites on the Internet. Users may opt out of personalized advertising by visiting Ads Settings.

Ads help to keep molbiotools up, running and evolving, but please do not click them repeatedly during a session, thank you.

Ads by Google

Probabilities

Clear
Calculate

# Poisson Distribution

Independent random events occuring in a defined time interval or a defined length, area or space volume follow Poisson distribution with parameter λ equal to the average number of events per the defined time, length, space or volume unit. The probability P of seeing exactly x events during the defined time interval or in the defined length, space or volume unit is given by the formula:
 P(X=x) = e-λ λx x!

λ≥0, x≥0

Calculator (fill all fields and click 'Calculate'):

Expected (average) number of events:λ =

Calculate the probability of x events:
x =
Calculate the total probability of numbers of events from the interval x1 - x2:
x1 = x2 =

P(X = x):

P(X ≤ x):

P(X ≥ x):

Clear
Calculate

# Binomial Distribution

Binomial distribution of probability describes likelihoods of all possible outcomes of n successive trials where in each trial there is the same probability p of "success" (i.e. of a defined result like e.g. a head when tossing a coin). The probability P of seeing exactly x successes in n successive trials is given by the formula:
 P(X=x) = n! x!(n - x)! px(1-p)n-x

n>0, 0≤x≤n, 0≤p≤1

Calculator (fill all fields and click 'Calculate'):

Number of trials:n =

Probability of success in one trial:p =

Calculate the probability of x successes in n trials:
x =
Calculate the total probability of numbers of successes from the interval x1 - x2:
x1 = x2 =

P(X = x):

P(X ≤ x):

P(X ≥ x):

Mean:

Clear
Calculate

# Hypergeometric Distribution

Hypergeometric distribution describes the probability of x successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly M objects with that feature, wherein each draw is either a success or a failure:
P(X=x) =
 ( M x ) ( N-M n-x )
 ( N x )

N>0, M>0, M≤N, 0<n≤N, 0≤x≤M, x≤n

Calculator (fill all fields and click 'Calculate'):

Total population size:N =

Subpopulation size:M =

Sample size:n =

Calculate the probability of x successes:
x =
Calculate the total probability of values of x from the interval x1 - x2:
x1 = x2 =

P(X = x):

P(X ≤ x):

P(X ≥ x):

Mean:

Clear
Calculate

# Geometric Distribution

The geometric distribution gives the probability that the first occurrence of a success requires x independent trials, each with the success probability p. The probability P that the x-th trial is the first success is described by the formula:
 P(X=x) = p(1-p)x-1

x>0, 0<p<1

Calculator (fill all fields and click 'Calculate'):

Probability of success in one trial:p =

Calculate the probability of x trials being required for the first success to occur:
x =
Calculate the total probability of all values x from the interval x1 - x2:
x1 = x2 =

P(X = x):

P(X ≤ x):

P(X ≥ x):

Mean:

Clear
Calculate

# Negative Binomial Distribution

Negative binomial distribution describes the probability that the x-th independent trial will be the k-th success provided each success has the same probability p:
 P(X=x) = ( x-1 k-1 ) (1-p)x-k pk
Alternatively, the distribution describes the probability of the next independent trial being the k-th success after a fixed number r of failures have occured:
 P(k, r) = ( k+r-1 k-1 ) (1-p)r pk

x>0, k>0, x≥k, r≥0, 0<p<1; x = k + r

Calculator (fill all fields and click 'Calculate'):

Probability of success in one trial:p =

Number of successes:k =

Calculate the probability that the x-th trial will be the k-th success:
x = , or alternatively, set the number of failures:r =
Calculate the total probability of all values x from the interval x1 - x2:
x1 = x2 =

P(X = x):

P(X ≤ x):

P(X ≥ x):

Mean:

### Tool Description

Probabilities Calculator is a free online tool for calculations of probabilities of events following one of the most common discrete probability distributions:

• Poisson Distribution
• Binomial Distribution
• Hypergeometric Distribution
• Geometric Distribution
• Negative Binomial Distribution

Ads by Google

Ads by Google