Question

Come up with an example scenario in which you would have a binomial probability distribution to work with.

Answer 1

Suppose, the probability of baby being a boy is 0.5.

Suppose we randomly select 5 babies.

Each outcome or trial is independent from each other.

Suppose we have to find the probability that exactly two babies will be boy.

That is, we have to find P(X=2)

For the above example, we are given

n = 5

p = 0.5

q = 1 – p = 1 – 0.5 = 0.5

Formula for binomial distribution is given as below:

P(X=x) = nCx*p^x*q^(n – x)

P(X=2) = 5C2*0.5^2*0.5^(5 – 2)

P(X=2) = 10*0.5^2*0.5^3

P(X=2) = 0.3125

Required probability = 0.3125