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Can you find the fallacy?

Dany has a square sheet and a pen. He decides to close his eyes and randomly make a spot on the square sheet. Say he hits the centre in his first try. But as there are infinitely many points on the sheet, the probabability of him hitting the centre is zero. And we know that if an event E has probability zero, it cannot happen. So how come Dany was able to hit the centre and has cause an event that had probabability=0?

So, 'Can you find the fallacy?'.

Note by Dhruv Bhasin
2 years, 9 months ago

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Well Dhruv, before explaining where the fallacy in your problem lies, let me first recapitulate the classical definition of probability of an event, which has been erroneously used in this problem:"If there are 'n' mutually exclusive, exhaustive and equally likely outcomes, or event points in the finite sample space of an experiment, and 'm' of them are favorable to an event A, then the mathematical probability of event A is given by:\[P(A)=\frac { m }{ n } \]" What you have done is you have considered n to be infinity and m to be 1, and hence found out P(A) to be zero. Well, one upon infinity is not zero actually, it is an infinitesimally small quantity. But even that argument doesn't arise here, as the very consideration of n to be infinity is forbidden within the purview of classical probability. So, you cannot use the classical definition here (which actually talks of experiments with finite sample spaces), and there lies your fallacy.

Kuldeep Guha Mazumder - 2 years, 6 months ago

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