# Statistics - Poisson distribution question.

1. Apr 29, 2013

### peripatein

Hi,
1. The problem statement, all variables and given/known data
I am somewhat perplexed by the proposed solution to the following Statistics problem and was hoping one of you might be willing to help me settle this:
An operator receives phone calls between 8AM and 4PM at an average rate of 20 calls/hour. No call was received during the first 3 minutes. What is the probability that we shall have to wait at least one more minute before the first call is received?

2. Relevant equations

3. The attempt at a solution
Now, the book states it ought to be P(T≥1) = 1 - FT(1) = e-1/3.
My question is, why should it not have been 1 - [F(4) - F(3)], i.e. the complement of a call received between the 3rd and 4th minutes?
I'd appreciate it if any of you could explain this to me.

2. Apr 29, 2013

### Ray Vickson

If T is the time of the first arrival, you want P{T > 4 | T > 3}, because you are told that the event {T > 3} occurred.

3. Apr 29, 2013

### peripatein

Thank you, Ray! It's clearer now :-).