Your Approach

@Marce Puente correctly points outin the question comments that retaining an exact percentage of elements is impossible, at least for smaller list sizes.

the idea of “exact percentage” is already wrong, imagine such a list: [ 10, 5, 1 ] and you want to keep it to *50%, what would you put, an item and a half, no, you have to set a tolerance, which will be determined by the number of item's.

For larger input sizes the rounding error decreases.

Another problem, as the busybee pointed out, is that discarding elements with a chance is not guranteed to return a stable amount of elements.

To illustrate that, here are 10 sets of random numbers between 0 and 100 (I noted the number of elements that would be retained given percentageToRetain = 30 in brackets):

0 64 93 11 77 13 82 87 8 68 (4 retains)
77 60 39 97 64 46 33 42 87 79 (0 retains)
26 91 0 32 49 31 15 7 2 7 (5 retains)
95 90 38 10 70 37 32 17 82 98 (2 retains)
11 43 96 58 10 40 30 4 40 54 (3 retains)
2 66 86 87 17 88 92 64 10 79 (4 retains)
3 86 75 51 30 37 2 96 49 89 (2 retains)
9 10 23 84 52 28 32 14 12 33 (5 retains)
53 91 54 66 28 61 67 35 45 70 (1 retains)
3 77 79 24 37 60 6 80 8 39 (4 retains)

My suggestion

1. calculate the.number of elements you wish to retain: int numberOfElementsToRetain = (int) (source.size() * percentageToRetain / 100.0);
2. make a copy of the input list to a known mutable type (you can skip this step if the input is guranteed to be mutable & you don't mind ruining it)
3. shuffle it
4. copy the first numberOfElementsToRetain elements to a new list & return that.

Thus we get:

public static <E> List<E> retainNumberOfElementsRandomly2(List<E> source, int percentageToRetain){
    int numberOfElementsToRetain = (int) (source.size() * percentageToRetain / 100.0);
    ArrayList<E> defcopy = new ArrayList<>(source);
    
    Random r = new Random();
    
    Collections.shuffle(defcopy, r);

    List<E> result = new ArrayList<>(numberOfElementsToRetain);
    
    for(int i = 0; i < numberOfElementsToRetain; i++){
        result.add(defcopy.get(i));
    }
    
    return result;
}