please answer only number d) One machine can produce three different types of screws S1, S2, S3. One and the same variety is always produced per work shift. The shares in production are 30% for S1, 45% for S2 and 25% for S3. Unfortunately, the machine does not work without any problems. The probability of a fault-free layer is 91% for type S1, 95% for S2 and 85% for S3. a) What is the probability that a shift will not have a disruption? b) A fault occurred during a shift. What is the probability that S3 grade was produced during this shift? c) What would have to be (instead of 85%) the probability of an interference-free shift in the production of type S3 in order to increase the probability of an interference-free shift from sub-task a) to 92.5%? d) What is the probability that a shift will be free of faults if grade S2 is not produced during this shift?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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please answer only number d)
One machine can produce three different types of screws S1, S2, S3. One and the same variety is always produced per work shift. The shares in production are 30% for S1, 45% for S2 and 25% for S3. Unfortunately, the machine does not work without any problems. The probability of a fault-free layer is 91% for type S1, 95% for S2 and 85% for S3. a) What is the probability that a shift will not have a disruption? b) A fault occurred during a shift. What is the probability that S3 grade was produced during this shift? c) What would have to be (instead of 85%) the probability of an interference-free shift in the production of type S3 in order to increase the probability of an interference-free shift from sub-task a) to 92.5%? d) What is the probability that a shift will be free of faults if grade S2 is not produced during this shift?

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