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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