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.

Thank you in advance.

  • $\begingroup$ You need to find the probability that more than 60 people voted for A,B,C,D combined (100-40). The number of A,B,C,D counted votes has a Poisson distribution with parameter 60 x 2 x 0.55. Use this parameter to calculate the probability P(X>60). $\endgroup$ – Zahava Kor Apr 12 '18 at 3:01
  • $\begingroup$ @ZahavaKor This ignores the dependence between the votes for the different parties. $\endgroup$ – Knarpie Apr 12 '18 at 9:05
  • $\begingroup$ No it doesn't - it only assumes that the decisions of the different people are independent. $\endgroup$ – Zahava Kor Apr 12 '18 at 22:27
  • $\begingroup$ 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 $\lambda = 66$ $\endgroup$ – Nicklovn Apr 26 '18 at 17:47

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