<div class="jumbotron">
            <h1>Работа с радиокнопками</h1>
            <div class="btn-group btn-group-toggle" data-toggle="buttons">
                <label class="btn btn-secondary active bg-danger">
                    <input type="radio" name="options" id="option1" autocomplete="off" value="red"> Красный
                </label>
                <label class="btn btn-secondary bg-primary">
                    <input type="radio" name="options" id="option2" autocomplete="off"  value="blue"> Синий
                </label>
                <label class="btn btn-secondary bg-success">
                    <input type="radio" name="options" id="option3" autocomplete="off"  value="green"> Зеленый
                </label>
            </div>
            <button type="button" class="btn btn-primary btn-sm btn-block" id="checks">Применить</button>
        </div>

    var radio = document.getElementsByName('options');
    for ( var i=0; i<radio.length; i++ ){
        radio[i].onchange = f2;
    }
    function f2() {
        console.log(this.value);
    //Получаем this.value

    }
    document.getElementById('checks').onclick = checkRadio;

    function checkRadio() {
        var b = document.getElementsByName('options');
        for ( var i=0; i<b.length; i++){
            if ( b[i].checked ){
                document.body.style.backgroundColor = 'red';
            }
        }
    }