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Insects of a certain type lay eggs on leaves such that the number of eggs on a given leaf has a Poisson distribution with mean 1. For any given leaf, the probability is 0.1 that it will be visited by such an insect, and leaves are visited independently of each other. (a) What is the probability that a given leaf has no eggs? (b) If a leaf is inspected and has no eggs, what is the probability that it has been visited by an insect? (c) If 10 leaves are inspected and none have any eggs, what is the probability that at least one leaf has been visited by an insect? .

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