Marge is an ordinary woman; she is no genius or a mathematician and she would love to earn some easy money. She had been observing how roulette was being played at the casino and she had discovered an apparently foolproof system of getting rich playing it. She noticed that it was quite common for the ball to fall into only black or only red slots during consecutive spins of the wheel. But the ball falling into the same color for 5 times in a sequence was unusual, and rarer it was for the ball to fall into the same color for six times or more in a row. As a matter of fact, she observed this happen only a couple of times in an entire day.
Hence her plan was to observe the ball falling into the same color for 5 times in a row, and then bet the next spin of the wheel on the other color, confident that her chance of winning was very high than losing. Can Marge afford to believe so?
I wracked my brain for a bit, struggling to find a flaw in her reasoning. You see I'm no mathematician myself, and as much as I tried to recall my classes on Logic and Probability, I really couldn't find anything amiss. And when I finally resigned and read what Baggini had to say, I still didn't get it!! Call me hopeless with Math. So I read it again, carefully, very carefully, and then the bulb finally glowed.
Since I've essentially not been successful in cracking or reasoning this puzzle myself, I don't want to merely repeat Baggini's reasoning. I will leave this as a fresh puzzle to anyone who chances by this article. But a little hint : we often miss out on subtle details of a problem due to our inevitable urge and selective processing, to look for what we want to find...
Hence her plan was to observe the ball falling into the same color for 5 times in a row, and then bet the next spin of the wheel on the other color, confident that her chance of winning was very high than losing. Can Marge afford to believe so?
I wracked my brain for a bit, struggling to find a flaw in her reasoning. You see I'm no mathematician myself, and as much as I tried to recall my classes on Logic and Probability, I really couldn't find anything amiss. And when I finally resigned and read what Baggini had to say, I still didn't get it!! Call me hopeless with Math. So I read it again, carefully, very carefully, and then the bulb finally glowed.
Since I've essentially not been successful in cracking or reasoning this puzzle myself, I don't want to merely repeat Baggini's reasoning. I will leave this as a fresh puzzle to anyone who chances by this article. But a little hint : we often miss out on subtle details of a problem due to our inevitable urge and selective processing, to look for what we want to find...
