(b) Records show that 6% of blood samples tested for a certain condition test positive. Assuming that whether or not a blood sample tests positive is independent of whether or not any other blood sample tests positive, calculate by hand the following probabilities correct to four decimal places. In each case, state clearly the probability model that you use (including the values of any parameters) and show your working. (i) The probability that out of 20 samples tested, at least three will test positive. [6] (ii) The probability that the first blood sample that tests positive tomorrow will be the ninth sample tested. [3] (c) The number of flaws in a fibre optic cable follows a Poisson distribution with parameter A = 1.25. Calculate by hand the probability that there are two or fewer flaws in such a fibre optic cable, giving your answer correct to three decimal places. Show your working. [3]