Suppose that S consists of all half-open intervals on (0, 1) of
form [(k - 1)/1000, k/1000) fork= 1, 2, ••• , 1000. Label the
kth interval ask and define f(k) = 1/1000 fork= 1, 2, ••• ,
1000.
(a) What probability does f(k) assign to the intervals
with union (0, 0.230)? [O, 0.500)?
(b) What probability does f(k) assign to the intervals
with union (0, 0.250)? (0.250, 0.500)? (0.75, 1.00)?