A quality control inspector DVD players for a complete inspection as they come off the assembly line.
It is known that 10% of all the items are defective.
Also, 60% of all defective items and 20% of all good items undergo a complete inspection.
a) if a randomly selected DVD player undergoes a complete inspection,what is the probability it is defective?
b)if a certain dvd pLayer did not undergo a complete inspection,what is the probability it is not defective?
It’s been a while since I have problems like these. Any nudging towards the process would be appreciated!
My work:
a) since 10% of the items are known to be defective and 60% of defective items undergo a complete inspection, the probability of a randomly selected DVD player to be inspected that is defective is 1/10*6/10 = 6%
In your attempt, you've ignored the fact that even good items can be inspected. In fact, by this calculation, you're answering the question "what is the probability of that a disc selected out of the complete sample space underwent inspection and was defective?" However, in the given question, the sample space is restricted to only those items which underwent inspection.
Sure, here you go:
For part (a):
Let $x$ be the total number of the items. Then, you should note that $0.1x$ are defective items (given: "It is known that 10% of all the items are defective."). So, $0.6\cdot0.1x=0.06x$ items undergo complete inspection and are defective, while $0.2\cdot0.9x=0.18x$ items undergo complete inspection and are good. Can you solve part (a) now?
Solution below:
The other part (b) is similar to part(a), and understanding (a) you should be able to solve (b).
Hope it helps!
EDIT: Solution for part (b)