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99% of machines function correctly at a factory and 1% are faulty. A robot comes in for quality control and correctly accepts and rejects machines 99% of the time and is wrong 1% of the time. The accepted machines are sold. Of the machines that are sold, what percentage are faulty?

I think the answer given is absolutely absurd and doesn't seem right at all.

I think the answer is 0.01%

Any help is appreciated!

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    what is the answer given and why do you think it's absurd? Also this is worded kinda funny, but I think the intent of the question is clear. Is an equivalent question "a factory makes cars and 1% of the cars are fault. After each car is made, it is inspected and the inspector correctly labels it faulty or not faulty 99% of the time. What percentage of faulty cars are labeled not faulty?" – 2017-01-10
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    Often these questions can be counterintuitive but the wording is very important. – 2017-01-10
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    The answer is 50%... Yes that's viable – 2017-01-10
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    I think a bit more than $0.01\%$ because the $1\%$ of working machines are rejected. – 2017-01-10
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    Of 10,000 cars 9,900 are good of which 99 are rejected. 100 are bad of which 99 are rejected. Therefore 50% of the rejects are good. – 2017-01-10
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    Well, what if the inspector had no skills and just labeled all the cars not faulty. What would their correctness % be then? Do you see another way to think about this? – 2017-01-10
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    @spaceisdarkgreen That's why the question states that the inspector correctly judges a machine to be faulty or not faulty 99% of the time – 2017-01-10
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    I'm just saying the issue is probably in the wording. Or they meant to ask about false positives, per Mark – 2017-01-10
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    You can solve this by applying Bayes theorem: $$P(\text{machine broken}\mid \text{machine gets approved}) = \frac{P(\text{machine gets approved}\mid \text{machine broken})P(\text{machine broken})}{P(\text{machine approved})}$$ – 2017-01-10
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    Generally speaking, in situations like this one, if the fraction of the population that is bad is small, you’ll get a surprisingly large fraction of false positives from what appears to be a very accurate test. This is why, for instance, blindly screening *everyone* for a rare disease can be counterproductive. – 2017-01-10

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It can be helpful to draw a diagram for this type of problem:

enter image description here

The green region represents functional machines that are also accepted—true positives—and the purple region represents non-functional machines that are accepted—false positives. The two red regions represent the rejected machines. The one on the right side of the diagram is non-functional machines that have been rejected correctly, while the region at the top of the diagram is the functioning machines that have been incorrectly rejected. You can see that the two regions are the same size, so half of the rejected machines are in fact functional. If you increase the fraction of functional machines overall, you will see that, counter to intuition, the rejection error rate actually increases: the top red region becomes larger than the right-hand red region and so a larger fraction of the total red area than before.

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As noted in the comment, If $N$ is the total number of machines produced, the number of sold machines is $$ \frac{99}{100}\cdot\frac{99}{100}N+\frac{1}{100}\frac{1}{100}N=\frac{9802}{10000}N $$ $\frac{N}{10000}$ of which are faulty, so the percentage of faulty on sold is $$ \frac{1}{9802}=0,010202..\% $$

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    Thank to the downvote I correct the stupid mistake ! – 2017-01-10