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The backoff torque required to remove bolts in a steel plate is rated as high, moderate,...

The backoff torque required to remove bolts in a steel plate is rated as high, moderate, or low. Historically, the probability of a high, moderate, or low rating is 0.61, 0.25, or 0.14, respectively. A sample of 15 bolts are selected for testing. Let X, Y, and Z denote the number of bolts that are independently rated as high, moderate, and low, respectively. Determine the following probabilities.
(a) P(X = 11, Y = 2, Z = 2)
(b) P(X = 7 | Y = 4)
Math   Statistics-And-Probability   
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