Aquality-control program at a plastic bottle production line involves inspecting finished bottles for flaws such as microscopic holes. the proportion of bottles that actually have such a flaw is only 0.0002. if a bottle has a flaw, the probability is 0.994 that it will fail the inspection. if a bottle does not have a flaw, the probability is 0.98 that it will pass the inspection.

if the bottle fails inspection, what is the probability that it has flaws?