# Poisson Process: In a small parliamentary election, votes are counted according to a Poisson process at the rate of 60 votes per minute

In a small parliamentary election, votes are counted according to a Poisson process at the rate of 60 votes per minute. There are six political parties, whose popularity among the electorate is shown by this distribution.

$$\begin{matrix} A & B& C&D&E&F \\ 0.05 & 0.30 & 0.10&0.10&0.25&0.20 \\ \end{matrix}$$

In the first 2 minutes of the vote tally, 40 people had voted for parties E and F. Find the probability that more than 100 votes were counted in the first 2 minutes.

I honestly need help starting this. If it had simply been, "40 votes were counted in the first 2 minutes. Find the probability that 100 votes were counted in the first 4 minutes" I would easily solve it. I'm honestly not sure how to format this using the distribution shown.

• Sorry this is late. I was just reviewing the problem and tried writing, $P(N_2 > 60) = 1-P(N_2 \le 60) = 1 - \sum_{i=0}^{60} \frac{e^{-120}(120)^i}{i!}$ But this gets me something pretty much equal to 0. Note, for above I do use parameter $\lambda = 66$ – Nicklovn Apr 26 '18 at 17:47