Poisson distribution and binomial distribution questions

3.
(a)Write down the binomial distribution for x successes in n independent trials each with probability p of success.

(b) Define the Poisson probability distribution with mean ?.

(c) Two rivets are drawn at random from a box containing ten rivets, three of which are defective.
(i) After the first rivet is chosen it is put back into the box and then another is chosen. Find the probability that exactly one of these is defective.
(ii) Find the probability that exactly one is defective if there is no replacement.

4.
(a) Define the Poisson probability distribution with mean p.

(b) A tool hire shop has six lawn mowers which it hires out on a daily basis.The number of lawn mowers requested per day follows a Poisson probability distribution with mean 4.5. Find the probability that:

(i) exactly three lawn mowers are hired out on any one day;
(ii) all lawn mowers are in use on any one day.

At what point are you stuck?

If your notes or textbook aren't helpful, try reading wikipedia's article on the binomia and poisson distributions. Then explain here what you think you understand, and what you are still confused about.