It's the least I could do ....

Suppose \(w,x,y\) and \(z\) are random real numbers chosen independently and uniformly from the interval \([0,1].\)

If the expected value of the smallest of \(w,x,y,z\) is \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, then find \(a + b.\)

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