How to check if any checkbox has been selected

I would like to see if any checkbox in a particular div has been selected, so as to proceed with a multiphase form I am working on. Currently whether a checkbox is selected or not, I am getting the alert "Tile selected".

HTML code

<div class='material' id='material1'>
     <a class='product'><div class='tiles_bg' style='background:url(media/images/tile2.jpg);'><input class='select_all' id='tile' type='checkbox' name='1marm' value='Verde Guatemala'></div><p>Verde Guatemala</p></a>
     <a class='product'><div class='tiles_bg' style='background:url(media/images/tile1.jpg);'><input class='select_all' id='tile' type='checkbox' name='1marm' value='Bianco Carrara'></div><p>Bianco Carrara</p></a>
</div>

<button type="button" class="nasta" onClick="processStep1()">Nasta</button>

jquery code

var tile;
function _(x){
    return document.getElementById(x);
}

function processStep1(){
    tile = _("tile").value;
    if(!("tiles_bg input:checked").length) {
    /*  _("step1").style.display = "none";
        _("step2").style.display = "block"; */
        alert(tile);
    } else {
        alert("Tiles selected");    
    }
}