The strength of a chemical solution is measured on a scale between 0 and 1, with values smaller than 0.5 being too weak, values between 0.5 and 0.8 being satisfactory, and values larger than 0.8 being too strong. If chemical batches have strengths that are independently distributed according to a beta distribution with parameters a = 18 and b = 11, what is the probability that if 10 batches are produced, exactly 1 batch will be weak, 1 batch will be strong, and the other 8 batches will all be satisfactory? (This problem is continued in Problem 5.3.11.)