Question 1192461
.
<pre>

The cube root of the number 574 is  {{{root(3,574)}}} = 8.31...


It means that there are 1+8 = 9 perfect cubes from 0 to 574, inclusive.


Therefore, the probability that a number chosen randomly from the set {0,1,2,3,...,574} is a perfect cube is


    P = {{{9/575}}} = 0.015652174   (rounded).    <U>ANSWER</U>
</pre>

Solved.