Question

Records show that 8% 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 to three significant figures. In each case, state clearly the probability model that you use (including the values of any parameters). (i) The probability that, out of 20 samples tested, at least four will test positive. [7] (ii) The probability that the first blood sample that tests positive tomorrow will be the tenth sample tested.