question 1 (A and B)

Question 1 (a) A factory produces components of which 2% are defective. The components are packed in a box of 8. A box is selected at random, (i) Find the probability that the box contains exactly one defective components. (1 mark) (ii) Find the probability that there are at least 2 defective components in the box. (3 marks) (iii) Find the mean and standard deviation of the defective components. (2 marks) (b ) The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. (1) Find the probability that there will be exactly 3 incidents in 6 months. (1 mark) (1i) Find the probability that there will be no more than 2 incidents in a year