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In a small pub there are two large tables. One evening, one table is reserved for...

In a small pub there are two large tables. One evening, one table is reserved for a Hungarian party and the other one for a Scottish party, and no else is allowed to enter the pub that night. After the pub opens at 8pm, Hungarians arrive one by one as a Poisson process with rate 4 and Scots arrive independently as a Poisson process with rate 5, where time is measured in hours. Justify your answer to the following question.

If we know that exactly 7 people arrived between 9pm and 10pm, what is the probability that 25 people arrived between 8pm and 11pm

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