I'm wondering if my answer for C would be correct and if I was understanding A correctly? I heard drawing venn diagram could help but I'm not sure how to convert the numbers to a diagram.
A quality-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 0.995 that it will fail the inspection. If a bottle does not have a flaw, the probability is 0.99 that it will pass the inspection.
$P(F)=$ fails inspection
$P(P)=$ Passes inspection
$P(f)=$ has flaw.
a. If a bottle fails inspection, what is the probability that it has a flaw?
$P(F\cap f) = P(F) \times P(f|F)$
c. If a bottle passes inspection, what is the probability that it does not have a flaw? $P(P \cap f^c) = \frac{(0.99)}{(0.995)} = 0.9949$