The strength of a chemical solution is measured on a scale

Chapter 4, Problem 4.8.10

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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 ten batches are produced, exactly one batch will be weak, one batch will be strong, and the other eight batches will all be satisfactory? (This problem is continued in 5.3.11.)

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