Saltar la navegación

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 probability
Example: 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