Choose hypergeometric or binomial sampling from replacement rules

A jar contains 10 blue and 8 red marbles. Five marbles are randomly drawn from the box, one by one and without replacement.

(i) Explain why it is inappropriate to model the number of blue marbles by a binomial distribution.1 mark

(ii) Find the probability that exactly three marbles are blue.3 marks

Another jar contains 20 blue and 12 red marbles. $n$ marbles are randomly drawn from the box, one by one and with replacement. The number of red marbles drawn is denoted by $R$.

(iii) Given that the mean of $R$ is 4.5, find $n$ and $P(R>4)$.3 marks

(iv) Given instead that $P(R=0\text{ or }1)<0.01$, write down an inequality for $n$ and find the least value of $n$.3 marks