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?

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?