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The number of red and blue cars that go through a given intersection in an hour is a Poisson-distributed random variable with $\lambda$ = 10. What is the probability, conditionally, that at most three cars that go through the intersection are red given that ten blue cars entered in that hour?

I should note, I understand how the Poisson distribution works, but I am not sure how to do it conditionally.

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Are the numbers of each Poisson distributed? And are the random variables independent? Or is it that the total has Poisson distribution? If so, are red and blue equally likely (implausible)? – André Nicolas May 1 at 15:37
@AndreNicolas There does not seem to be any information on independence or whether it is the total that has Poisson distribution. There was another section I left out from the question which notes: What assumptions were made? I assume the idea is to construct the rest of the missing information arbitrarily as it is very much an applied probability question. Sorry for not being clearer. – user73041 May 1 at 15:42
Presumably the number of cars is Poisson, and the color is independent with some fixed probability? – copper.hat May 1 at 15:51
Yes, that seems right. Perhaps for simplicity perhaps we can say that they are equally likely? The question seems to be partly about making some semi-reasonable assumptions. – user73041 May 1 at 15:55
Is it possible to provide the source of the question (instead of making people wonder what is in it)? – Did May 1 at 20:07
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