MathUtils.java

    public static <T> T weightedRandom(ObjectIntMap<T> objectsWithWeights) {
        int totalWeight = 0;
        for (ObjectIntMap.Entry<T> entry : objectsWithWeights) {
            totalWeight += entry.value;
        }

        int random = MathUtils.random(1, totalWeight);

        int weightCovered = 0;
        for (ObjectIntMap.Entry<T> entry : objectsWithWeights) {
            weightCovered += entry.value;
            if (random <= weightCovered) {
                return entry.key;
            }
        }

        throw new GdxRuntimeException("Could not determine a random object by the given weights.");
    }