Which probability model would you use to describe the number of customers served at a certain California Pizza Kitchen until the first customer orders split pea soup?
A)Binomial
B)Geometric
C)Uniform
D)Poisson

Question

Quizplus · Accepted Answer

The question is asking for the probability model to describe the number of customers served until a certain event occurs (the first customer orders split pea soup). This is a classic example of a geometric distribution, where each customer arriving has a certain probability of ordering split pea soup (which is assumed to be independent of previous customers) and we're interested in the number of customers we'll have to serve until the first one orders it. The other options are not appropriate for this scenario: 
- A binomial distribution requires a fixed number of independent trials with two possible outcomes each (success or failure), but the number of customers served is not fixed and there can be more than two possible outcomes (e.g. the customers could order different dishes). 
- A uniform distribution describes a situation where every outcome in a given range has the same probability, but here the probability of a customer ordering split pea soup is not the same as the probability of a customer ordering a different dish. 
- A Poisson distribution is used to model the number of rare events that occur randomly in a certain time frame, but here we don't have a specific time frame and the event we're interested in (a customer ordering split pea soup) is not necessarily rare.

Which Probability Model Would You Use to Describe the Number