# Probability of Poisson event happening twice, consecutively

1. Oct 25, 2015

### cmkluza

1. The problem statement, all variables and given/known data
The number of telephone calls, T, received each minute can be modelled by a Poisson distribution with a mean of 3.5.

Find the probability that at least three telephone calls are received in each of two successive one-minute intervals.
2. Relevant equations
$P = \frac{e^{-μ}μ^x}{x}$

3. The attempt at a solution
I realize that I can calculate the probability of getting three phone calls during one minute using $\frac{e^{-μ}μ^x}{x} = \frac{e^{-3.5}3.5^3}{3}$ (or, more simply, by using a calculator), but I don't currently have any intuition on how to find the probability of finding the probability of this happening twice, consecutively. Can anyone give me any suggestions on how to think about this in order to arrive at an answer? Thanks!

2. Oct 25, 2015

### Ray Vickson

You are not asked about 3 calls in each minute; you are asked about at least 3 calls in each minute; that is, in each minute the number of calls is 3 or 4 or 5 or 6 or ... .

3. Oct 26, 2015

### haruspex

After you have addressed Ray's point, consider whether the two events (calls in first minute, calls in second minute) are independent or correlated.

4. Oct 30, 2015

### cmkluza

Thanks, looks like I read the question a little too quickly. Anyhow, at least 3 just changes it to a cumulative distribution function, right?

It would appear that the events are independent. Based on the old example of tossing a coin, I'd guess that I find the probability of getting at least 3 calls, and square it?

5. Oct 30, 2015

### haruspex

Yes.

6. Oct 30, 2015