About 5 years ago, this question i got wrong in a maths test. there was a scale of 0-1 of probabilities, and the question was 'what is the chance of a black car being the first car of the day passing a certain point?' we're not given any extra information, nothing about the amount of cars or the colours of them, just this vague statement.
I put a pretty low amount, maybe 0.1, but the answer was somewhere around the 0.5 mark. the explanation for this was 'the car could either be black, or another colour, so around the 1/2 way mark'.
Can someone explain to me how this makes any sense? If this is seen as reasonable, then the chances of winning the lottery would be 1/2, as you would either win it or you wouldn't..... :P
I put a pretty low amount, maybe 0.1, but the answer was somewhere around the 0.5 mark. the explanation for this was 'the car could either be black, or another colour, so around the 1/2 way mark'.
Can someone explain to me how this makes any sense? If this is seen as reasonable, then the chances of winning the lottery would be 1/2, as you would either win it or you wouldn't..... :P
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That makes no sense. Your lottery analogy is correct. Some people seem to believe that if there are only two possibilities, they each have a 50% probability of occurring. But that's not true.
The answer is equal to the fraction of cars which are black, and I'd say 5-10% is in the right order of magnitude.
The only way that could kind of make sense is as a "Bayesian prior", the guess you make with no information whatsoever. In Bayesian probability theory, probabilities are degrees of belief, and they change as you get information. With no information whatsoever, a uniform distribution (all possibilities equally likely) is a plausible initial guess.
The answer is equal to the fraction of cars which are black, and I'd say 5-10% is in the right order of magnitude.
The only way that could kind of make sense is as a "Bayesian prior", the guess you make with no information whatsoever. In Bayesian probability theory, probabilities are degrees of belief, and they change as you get information. With no information whatsoever, a uniform distribution (all possibilities equally likely) is a plausible initial guess.