Question

Suppose the probability of a customer placing an order at a pizza place for a pepperoni pizza is 0.6, and for something else with probability 0.4. We assume if a customer calls the pizza place, he orders something, and that all incoming calls are indepen- dent. What is the probability that the pizza place will get the first pepperoni pizza order on the 4th call of the day?

Answer 1

The geometric distribution gives the probability that the first occurrence of success                   
requires k independent trials, each with success probability p.                  
p = 0.6   probability of a customer placing an order at a pizza place for a pepperoni pizza              
                   
Let X be the number of customer calls until the first pepperoni pizza is ordered (including the customer ordering pepperoni pizza)                  
X follows a Geometric distribution and the probabilities are given by                  
...............r = 1,2,3......
To find P(pizza place will get the first pepperoni pizza order on the 4th call)                  
that is to find P(X=4)                  

   P(X = 4) = 0.0384                  

P(pizza place will get the first pepperoni pizza order on the 4th call) =