[destus]

<button id="but_id">click me</button>
    <input type=radio name='radiobutton' value="1" id="labeled_1" />
    <input type=radio name='radiobutton' value="2" id="labeled_2" />
    <script>
        document.getElementById('but_id').onclick = function () {
            !!document.querySelector('input[type=radio]:checked') && alert("Функция вызвана");
        }
    </script>