The "Correct" answer for one of the 'BBC - The Big Risk Quiz' questions?
I've just completed the BBC Big Risk Quiz and I'm confused about what the correct answer should be for this question (it was the only one of the 'understanding risk' questions I got wrong (Clapping))
Note that this is a SPOILER ALERT!! for anybody who hasn't yet completed the quiz..
Initially I answered 95% because the lie detector is 95% accurate and would hold true irrespective of whether the person is the criminal or not (see the mini rant below).
5. A criminal hides in a room with 99 innocent people. You have a lie detector that correctly classifies 95% of people. You pick someone at random, wire them up to the machine, and ask them if they are a criminal. They say no, but the machine goes ‘ping’ and says the person is lying. What is the chance that you have caught the criminal?
Your answer: 95%. Correct answer: 17%.
I can see why the answer of 95% might be incorrect, since there is a 1/100 chance of selecting the criminal (1x criminal + 99x innocents) in the first place and then a 95/100 chance of the lie detector being correct, but this results in a 9.5% chance of having caught the criminal and not 17%, surely?
Can anybody clarify why 17% is listed as the 'correct' answer? I do not recall 9.5% being any of the options.
Mini rant: I really dislike how imprecise the questions are.. It doesn't specify that the person selected is from the pool of 100 people mentioned at the start.. There's a whole bunch of other examples of it throughout the test too..