Six random variables

Six variables xi x_i are chosen uniformly at random in the interval [0,1][0,1].

Find the probability that x1+x2+x3+x4+x5+x6<1. x_1 + x_2 + x_3 + x_4 + x_5 + x_6 < 1. If the answer is of the form ab\frac{a}{b}, where aa and bb are coprime positive integers, what is a+b?a+b?


Inspired by Brian Charlesworth
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