(a) A fair die with six faces is thrown six times. Calculate, correct to three decimal places, the probability of obtaining : (i) exactly three sixes ; (ii)...

(a) A fair die with six faces is thrown six times. Calculate, correct to three decimal places, the probability of obtaining :

(i) exactly three sixes ; (ii) at most three sixes.

(b) Eight percent of screws produced by a machine are defective. From a random sample of 10 screws produced by the machine, find the probability that :

(i) exactly two will be defective ; (ii) not more than two will be defective.