You and a friend are flipping a coin. It comes up heads 4 times in a row. You flip it again. Neither one of you is cheating and the coin is a normal coin. If you were to gamble on the outcome of the 5th flip, what would you do?
(a)Bet on tails (b)It doesn't matter, it's still 50/50 (c)Bet on heads
it would seem that (b) would be the answer they want, but in my mind (c) is easily the obvious choice
did you pass junior high school math?
What if it had said that it had landed on heads 50 times in a row instead of 4 times? Then I think the most correct answer is probably that the premise is wrong and either one of you is cheating or it is not a normal coin. But obviously if you accept the premises, then (b) is correct. If I had to bet on the next flip of the coin in this question, though, i'd be sure as hell to bet on heads, even though it 'doesn't matter'. Chances are, the coin is not a fair coin.
Yeah, b is probably the answer they want, c is what I would pick in real life, and if you accept the premise that the coin is normal and no one is cheating you should pick A because tails is slightly more likely than heads on a normal coin.
(c) is obviously correct. Different levels of understanding indicate different answers:
Super donk-- Tails is due. Semi-donk-- Heads is coming up a lot. Ordinary pro gambler, or someone who's read a mathbook-- It doesn't matter. Expert--Since it doesn't matter if the coin is fair, I'll bet Heads, in case my assumption that the coin is fair is wrong.