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 )
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..