Wire manufactured by a company is tested for strength. The test gives a correct positive result with

Jaqueline Kirby 2022-06-21 Answered
Wire manufactured by a company is tested for strength. The test gives a correct positive result with a probability of 0.85 when the wire is strong, but gives an incorrect positive result (false positive) with a probability of 0.04 when in fact the wire is not strong.
If 98% of the wires are strong, and a wire chosen at random fails the test, what is the probability it really is not strong enough?
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Answers (1)

Answered 2022-06-22 Author has 29 answers
Events - Strong wire P ( S ) Weak Wire P ( S ) Result = P ( T ) - true positive result
P ( S ) = 0.98 P ( S ) = 0.02 P ( T | S ) = 0.85 P ( T | S ) = 0.04
P ( S | T ) = ( P ( T | S ) × P ( S ) ) / [ ( P ( T | S ) × P ( S ) ) + ( P ( T | S ) × P ( S ) ) ]
P ( S | T ) = 0.85 × 0.98 / ( 0.85 × 0.98 + 0.04 × 0.02 ) = 0.8673 / 0.8681 = 0.9991 = 99.91
99.91 % times wires are strong when tested positive
For wires tested strong and result is weak = 1 P ( S | T ) = 1 0.99 = 0.01 = 1 % So, a wire chosen from suite of strong tested wire and comes out to be weak is 1 %
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New questions

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