- [Maximum mark: 9]
A biologist uses a wire frame to count the number of worms in a 1 m² section.
She models the number of worms found in each 1 m² section as following a Poisson distribution with mean 1.2.
(a) Find the probability of observing exactly one worm in one 1 m² section. [1]
(b) Find the probability of observing at least one worm in one 1 m² section. [1]
The biologist looks at 5 independent 1 m² sections.
(c) Find the probability of observing a total of five worms in 5 sections. [2]
(d) Find the probability of observing exactly one worm in all 5 sections. [2]
(e) Find the probability of observing at least one worm in exactly 3 of the 5 sections. [3]