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The next fills

ProbabilityEasy

Fills reach a desk from venue A and venue B as independent Poisson processes, at $2$ and $6$ fills per minute. What is the probability that the next $2$ fills both come from venue B? Give a fraction in lowest terms.

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Hint

In a merged stream each arrival has its own independent label.

Solution

Merged, each fill comes from B with probability $\frac{6}{2 + 6} = \frac{3}{4}$ , independently of the others.
So both do with probability $(\frac{3}{4})^{2} = \frac{9}{16}$ .

Answer: $\frac{9}{16}$

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