This problem picks up from 2-147. In 2-147 theprobability of at least one bolt i

Question

This problem picks up from 2-147.   In 2-147 theprobability of at least one bolt in a sample of 4 not beingcorrectly torqued was 0.718. The probability of all boltsbeing correctly torqued was 0.282. This problem adds that theprobability of a bolt being correctly identified as not torqued is0.95. The probability of a bolt being correctly identified astorqued is 1.00 (no errors in identification).   Thequestion is out of the 4 bolt sample, what is the probability of atleast one bolt being correctly indentified as nottorqued. I am stuck. This problem picks up from 2-147.   In 2-147 theprobability of at least one bolt in a sample of 4 not beingcorrectly torqued was 0.718. The probability of all boltsbeing correctly torqued was 0.282. This problem adds that theprobability of a bolt being correctly identified as not torqued is0.95. The probability of a bolt being correctly identified astorqued is 1.00 (no errors in identification).   Thequestion is out of the 4 bolt sample, what is the probability of atleast one bolt being correctly indentified as nottorqued. I am stuck.

Explanation / Answer

We'll take it one step at a time. The probability of all 4 bolts properly torqued is .282. The probability of a single bolt being being properly torqued isexpressed as X4 = .282. (.282) ^ (1 / 4) = .728723    : The probability that a single bolt is properlytorqued. 1 - .728723 =.271277         : The probability that a single bolt isimproperly torqued. .271277 * .95 =.257713      : The probabilitythat a single bolt is improperly torqued ANDidentified. 1 - .257713 =.742287         : The probability that there is not a single bolt improperlytorqued AND identified. .742287 ^4 =.303589          : The probability that all four bolts there is no boltimproperly torqued AND identified. 1 - .303589 =.696411         : The probability that at least one of four bolts isimproperly torqued AND identified. Does this make sense? Hope it helps!

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