Checkbox subcategories hidden until parent checkbox selected

I'm trying to get subcategory checkboxes to only display once the relevant parent checkbox has been selected.

At the moment I'm using the following code:

<script type="text/javascript">
$(document).ready(function () {
$("#listing_category-401 .children").css("display", "none");
$(".option").change(function () {

    if ($('checkbox[id="in-listing_category-401"] :checked').val() == "true") {
        $("#listing_category-401 .children").slideDown("fast");
    }
});
});