Question

At a certain breakfast restaurant, the probability of a customer ordering coffee is 0.8. When the restaurant seats two new customers, X is the number of customers ordering coffee. What is P(X=0)? Enter your answer, as a decimal, in the box. P(X=0) =

Answer 1

`P(X=0)=0.04`

Explanation:

In a binomial distribution probability, if probability of a success is `p` and that offailure is `q` (note that `q=1-p`), then probability of `x` successes out of `n` trials is `C_x^np^xq^(n-x)`.

Here `p=0.8` and hence probability of none of the two ordering a coffee is

`P(X=0)=C_0^2p^0q^2=1*(0.8)^0*(0.2)^2=1*1*0.04=0.04`