Three points X1, X2, and X3 are selected at random from an interval of length L. Find the probability that none of the three points are within a distance a of the left end where a < L. Solution P(a point lies within a distance \'a\' from the left end) = a/L P(a point doesn\'t within a distance \'a\' from the left end) = (L-a)/L P(none)= [(L-a)/L]^3.