# Probability: Poisson distribution involving customer arrivals

1. Feb 17, 2014

### sanctifier

1. The problem statement, all variables and given/known data

There are two stores A and B.

Customers can equally enter one of the two stores, i.e., for a specific customer, the probabilities she enters store A or B both are 0.5.

If the total number of customers in two stores has the Poisson distribution of parameter λ, then

Question 1: What is the probability that the number of customers in store A is non-zero and store B has no customers;

Question 2: What is the probability that the number of customers in store A is exactly 2 and store B has no customers.

2. Relevant equations

Poisson distribution: p(x)=λx/x! * e

3. The attempt at a solution

Comment: The probability that there are some customer in some store is 1 - p(0), then the probability that x customers entered store A is 0.5x, hence their product should yield the desired answer?

Comment: Similar strategy as answer 1.

Are these correct?

Last edited: Feb 17, 2014
2. Feb 17, 2014

### Ray Vickson

3. Feb 17, 2014

### sanctifier

Ray Vickson, thank you for your replay.

If answer (2) is correct, then answer (1) is p(1)*0.5 + p(2)*0.52 + p(3)*0.53 + ...

Is this correct?

If it is, then is there a concise form of the summation?

4. Feb 17, 2014

### Ray Vickson

Yes, and yes. For the latter, see https://www.efunda.com/math/exp_log/series_exp.cfm .