To solve this problem, we need to find the number of permutations that result in no president being matched with his term in office, and divide it by the total number of possible permutations.

The number of ways to choose a random permutation of the list is 24!, since there are 24 presidents.

To calculate the number of permutations that result in no president being matched with his term, we can use the principle of derangements.

A derangement is a permutation of a set in which none of the elements appear in their original position. Let's denote the number of derangements of a set with n elements as D(n).

For a set with n elements, the number of derangements can be calculated recursively using the formula D(n) = (n-1)(D(n-1) + D(n-2)), with D(0) = 1 and D(1) = 0.

For our case, we have n = 24, so we can calculate D(24) by applying the formula recursively:

D(24) = (24-1)(D(23) + D(22))
D(23) = (23-1)(D(22) + D(21))
D(22) = (22-1)(D(21) + D(20))
...
D(2) = (2-1)(D(1) + D(0))
D(1) = 0
D(0) = 1

Using this recursive calculation, we can determine that D(24) = 9,455,551.

Therefore, the probability that no president is matched with his term in office is given by D(24)/24!:

P = D(24)/24! = 9,455,551/24! ≈ 0.367879

So, the probability is approximately 0.367879, or about 36.79%.