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?
I am just newbie to probability math but want to solve it, can any tell me what all events are given from this? And how to identify them?
I found out that I am having trouble in finding events, if I find them, rest is easy.
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) = 0.85 x 0.98 / (0.85 x 0.98 + 0.04 x 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%