PROBABILITY

# binomial distribution

The

**binomial distribution**with parameters*n*and*p*is the discrete probability distribution of the number of successes in a sequence of*n*independent experiments (*p*=success probability).If

*X=B(n,p)*is a random binomial variable, the probability of getting k successes is:where

*q = 1 – p*= failure probabilityExample: the probability of obtaining a head with a loaded coin is 2/3. Calculate the probability of obtaining 6 heads if we flip this coin 10 times.

X = number of heads → X = B(10,2/3)

The parameters of a binomial distribution are:

In the example:

**Exercise**. The probability that a student from a specific school obtains a Baccalaureate certificate is 0.7. Calculate the probability that, in a group of ten students from this school:

a) all of them obtain the degree

b) at least two of them obtain the degree

Solutions: a) 0.0282; b) 0.999

Obra publicada con Licencia Creative Commons Reconocimiento No comercial Compartir igual 3.0