The Antarctic petrel is an important indicator bird species, and researchers

are interested in determining its abundance in the Shetland Islands in

Antarctica to measure the effects of global warming. According to the

researchers, the islands present on average, $1\mathrm{.}9$ petrels per square meter.

$12$ researchers separately visited these islands on independent occasions

and each counted the number of petrels over an area of $10m^2.$ Assume that

the number of petrels per square meter follows a Poisson distribution.

$($a$)$ For a researcher selected at random, what is the probability that they

saw no petrels?

$($b$)$ For a researcher selected at random, what is the probability that they

saw at least one petrel?

$($c$)$ What is the probability that exactly seven $($out of the $12)$ researchers

counted at least one petrel?