The worst-case time complexity of randomized quicksort is \(O(n^{2})\), which occurs in the rare scenario that the random pivot consistently results in an extremely unbalanced partition, such as dividing the array into a partition of size \(n-1\) and another of size \(0\). While this worst-case is possible, randomization makes it highly improbable. The expected or average-case complexity for randomized quicksort is significantly better, at \(O(n\log n)\).     

• Worst-case time complexity: \(O(n^{2})\). This happens when the randomly chosen pivot is consistently the smallest or largest element in the subarray. Each partition step would then only reduce the problem size by one element, leading to a linear number of recursive calls. 
• Expected (average-case) time complexity: \(O(n\log n)\). The randomization of the pivot selection makes it extremely unlikely to encounter the worst-case scenario consistently. On average, the pivot will divide the array into more balanced partitions, leading to the typical logarithmic behavior of Quicksort.