Hank sets up a bird table in his garden to provide the local birds with some food. Hank notices that a specific bird, a large magpie, visits several times per month and he names him Bill. Hank models the number of times per month that Bill visits his garden as a Poisson distribution with mean 3.1.

Using Hank's model, find the probability that Bill visits the garden on exactly four occasions during one particular month.

Over the course of 3 consecutive months, find the probability that Bill visits the garden on exactly 12 occasions.

Over the course of 3 consecutive months, find the probability that Bill visits the garden during the first and third month only.

Find the probability that over a 12-month period, there will be exactly 3 months when Bill does not visit the garden.

After the first year, a number of baby magpies start to visit Hank's garden. It may be assumed that each of these baby magpies visits the garden randomly and independently, and that the number of times each baby magpie visits the garden per month is modelled by a Poisson distribution with mean 2.1. Determine the least number of magpies required, including Bill, in order that the probability of Hank's garden having at least 30 magpie visits per month is greater than 0.2.