Two Students Are Walking Their Dogs Around a Park

Short Answer

Two students are walking their dogs around a park. Mary's dog sniffs a tree at a Poisson rate of 4 times per hour, while Antoine's dog sniffs a tree at a Poisson rate of 3 times per hour independently of Mary's dog. If Mary's dog sniffed the last 2 trees, what is the probability that Antoine's dog will sniff a tree next?