(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.
Explanation
(a) (i) p(exactly 3 sixes) = = = = = 0.0536 0.054. (ii) p(at most 3 sixes) = p(0 six) + p(1 six) + p(2 sixes) + p(3 sixes) = = = = (to 3 d.p) (b) p(a defective screw) = 0.08 ; p(non- defective screw) = 1 - 0.08 = 0.92. The binomial distribution = . (i) p(exactly 2 defective) = = = (ii) p(not more than 2 defective) = p(0 defective or 1 defective or 2 defective) = = = = (3 d.p)