1. At the Poisson Casino, two dice are rolled at random
times according to a Poisson process with parameter 𝜆. Find the probability that in [0, t]
every pair of dice rolled comes up 7.

2. Oak and maple trees are each located in the arboretum
according to independent spatial Poisson processes with parameters 𝜆O and 𝜆M, respectively.

(a) In a region of x square meters, find the probability
that both species of trees are present.

(b) In the arboretum, there is a circular pond of radius 100
m. Find the probability that within 20 m of the pond there are only oaks

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