I need help finding the R coding for the whole problem

Question 2: Suppose an insect visits a given leaf with probability p = 0.4. While there, the insect lays eggs that follow a Poisson distribution having mean parameter A=3. (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 five leaves are inspected and none have any eggs, what is the probability that at least one leaf has been visited by an insect? Write a simulation in R that models the number of eggs on 10,000 leaves based on the parameters p and A given above. (d) What is the proportion of leaves that have no eggs? (3) Among the leaves that have no eggs, what proportion of those leaves had been visited by an insect