Question

The probability that a customer's order is not shipped on time is 0.05. A particular customer places three orders, and the orders are placed far enough apart in time that they can be considered to be independent events. What is the probability that all are shipped on time

Answer 1

We want to find the following probability:

`P(X=3)`

And using the probability mass function we got

`P(X=3)=(3C3)(0.95)^3 (1-0.95)^(3-3)=0.857`

Explanation:

Let X the random variable of interest "number of orders on time", on this case we now that:

`X \sim Binom(n=3, p=1-0.05=0.95)`

The probability mass function for the Binomial distribution is given as:

`P(X)=(nCx)(p)^x (1-p)^(n-x)`

Where (nCx) means combinatory and it's given by this formula:

`nCx=(n!)/((n-x)! x!)`

We want to find the following probability:

`P(X=3)`

And using the probability mass function we got

`P(X=3)=(3C3)(0.95)^3 (1-0.95)^(3-3)=0.857`