Final answer:
The probability of selecting the worst possible pivot for quick sorting an array of 25 distinct elements is 2/25, which is 0.08 when rounded to two decimal places.
Step-by-step explanation:
The question is asking about the probability of selecting the worst possible pivot in the first round of partitioning in a quick sort algorithm, where the array has 25 distinct elements. When using quick sort, the worst possible pivot would be the highest or lowest element because it would result in the most unbalanced partition, meaning either one of the subarrays after partitioning would have 24 elements and the other would have none, leading to the worst-case time complexity.
The probability of selecting the worst possible pivot can be calculated simply because there are only two 'worst' positions out of the 25 available (the first and the last). Therefore, the probability P of choosing the worst pivot is given by the number of worst positions divided by the total number of possible positions:
P = 2/25 = 0.08. Thus, rounded off to two decimal places, the probability is 0.08.