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how to prove that the range probability lies between 0 to 1

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if suppose there are 10 students and the number of chocolates given to them is 10 then probability of each is 0.1.if there is only one student and he is given 10 chocolates then there is no competition for him so he gets the whole no. of chocolates that is 10/1 where as in the previous case it was 1/10.

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