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Bernoulli trials table

This online calculator calculates probability of k success outcomes in n Bernoulli trials with given success event probability for each k from zero to n.

person_outline Timur schedule2017-06-28 20:42:46

This online calculator calculates probability of k success outcomes in n Bernoulli trials with given success event probability for each k from zero to n. It displays result in table and on chart. This is the enhancement of Probability of given number success events in several Bernoulli trials calculator, which calculates probability for single k.

PLANETCALC, Bernoulli trials table

Bernoulli trials table

Digits after the decimal point: 3

Bernoulli trials

Tags:  Bernoulli Bernoulli trials binomial distribution events Math probability probability theory Statistics table trials
Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Bernoulli trials table

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Probability of given number success events in several Bernoulli trials

Gives probability of k success outcomes in n Bernoulli trials with given success event probability.

person_outline Anton schedule2016-04-02 18:55:11

For example we have a box with five balls : 4 white balls and one black. Every trial we take on ball and then put it back. How do we determine probability of taking black ball 2 times of 10 trials?

The experiment which has two outcomes "success" (taking black ball) or "failure" (taking white one) is called Bernoulli trial. The experiment with a fixed number n of Bernoulli trials each with probability p, which produces k success outcomes is called binomial experiment.
Probability of k successes in n Bernoulli trials is given as:
P_n(k)=C_n^k \cdot p^k \cdot q^n-k, \quad q=1-p where p – is a probability of each success event, C_n^k – Binomial coefficient or number of combinations k from n
The details are below the calculator.

PLANETCALC, Probability of k success events in n Bernoulli trials

Probability of k success events in n Bernoulli trials

Digits after the decimal point: 5

Probability
 

Probability of taking black ball in k first trials of n total trials is given as:
P=p^k \cdot q^(n-k) it’s a probability of only one possible combinations. According to combinatorics formulas the following k success combinations number is possible in n trials: C_n^k=\fracn!k!(n-k)! see Combinatorics. Combinations, arrangements and permutations .

Number of success events k in n statistically independent binomial trials is a random value with the binomial distribution, see: Binomial distribution, probability density function, cumulative distribution function, mean and variance

Tags:  Bernoulli Bernoulli trials binomial distribution events Math probability probability theory Statistics trials
Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Probability of given number success events in several Bernoulli trials

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  • Bernoulli trials table
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