# Probaballistic fun

Discrete Mathematics Level pending

Let $$\epsilon\equiv\frac{1}{N}$$ Choose a number at random between 0 and 1. Choose a second number between $$\epsilon$$ and $$\epsilon+1$$. Choose a third number between $$2\epsilon$$ and $$1+2\epsilon$$. Continue this process, until you choose an Nth number $$1-\epsilon$$ between and $$2-\epsilon$$. What is the probability that the first number you choose is the smallest of all the numbers? Assume that N is very large, and make suitable approximations. if the answer is in the form $$P\thickapprox\sqrt{\frac{a}{b^{2}N^{\frac{\sqrt{2}}{b}}}}$$ then find the value of a upto two digits

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