1. Niki is babysitting Hannah and Joshua all day today. Hannah cries at a Poisson rate of...

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1. Niki is babysitting Hannah and Joshua all day today. Hannah cries at a Poisson rate of 10 times per day. Joshua cries at a Poisson rate of 7 times per day independently of Hannah.

If it was Hannah who cried the last three times, what is the probability that the next baby who will cry is Joshua?

Hint: Due to the memoryless property of exponential random variables, it does not matter who cried last or how many times before.

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