The Tuffsteel Corporation manufactures bolts in various sizes. Today, 3 machines

Question

The Tuffsteel Corporation manufactures bolts in various sizes. Today, 3 machines are in operation. Machine A is producing 25% of the bolts, Machine B is producing 36% and Machine C is producing the rest of the bolts today. The probability that Machine A produces a defective bolt is 0.05. For Machine B, the probability that a bolt is defective is 0.04, while for Machine C the probability that a bolt is defective is 0.02.

e) Is whether the bolt is defective independent of which machine produced it? Support your answer mathematically.

Explanation / Answer

here from P(defective|machine A)=0.05 ; P(defective |machine B)=0.04 and

P(defective |machine C) =0.02

from probability of defective is different for all 3 type of machines therefore probability of defective depends on type of machine

hence bolt is defective is not independent of which machine produced it

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