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# Cambridge interview sample question... watch

1. A certain medical condition affects one in a thousand of the population. A screening procedure is developed that is 95% accurate. Discuss the probability that you have the condidtion if the screening procedure says that you do.
2. This seems a little easy for an interview question? There is simply a 2% chance you have the condition.
3. (Original post by Kolya)
This seems a little easy for an interview question? There is simply a 2% chance you have the condition.
I think it's intended to be a "trick question" in that some candidates may just say 95%. And the fact that the results of a test with 95% accuracy only gives you a 2% chance of actually having the medical condition is quite surprising, too.
4. I'm not very clever, and not applying to oxbridge.

Will someone just explain as to how its a 2% chance.

Ta. =]
5. Take 1000 people. 1 will be expected to have the condition. (999x5 + 1x95)/100 will be expected to be diagnosed, which is very close to 1000x5/100 = 50 - close enough, given the significant figures of the data. Hence 1 people will have the condition, 50 will be diagnosed, so there is a 1/50 = 2% chance of having the condition if you are diagnosed as having it.
6. Reminds me of a demonstration yesterday in the series of maths lectures at UCL...
7. In fact given this values the more accurate solution is 1.87% , but the algoritm is pretty much the same.

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Updated: November 29, 2012
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