An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is _______.

In quicksort partitioning of an array of $n$ distinct elements, the worst possible partitioning occurs when the pivot element is either the minimum or the maximum element of the array (resulting in an unbalanced subproblem split of sizes $0$ and $n-1$).

• Total number of elements, $n = 25$.

• Number of worst-case pivot positions = $2$ (the smallest element and the largest element).

Since the pivot is chosen uniformly at random, the probability is:

Thus, the probability rounded off to 2 decimal places is 0.08.