Search against a checkboxes field's options
Checkboxes / multiselect fields store to the database in a very query unfriendly way.
That's why I would really recommend to use categories, tags, lightswitches instead, if you intend to
query against these fields' values.

Here's what you'd have to do to search for entries with selected checkboxes field types' options. You basically have to get all relevant entries first,
go through them to check each checkbox option and store the element ID in case the entry is valid. Using this approach you end
up with an array of IDs which you can now query against.

{% set entries = craft.entries.section('news') %}

{% set query = craft.request.getQuery() %}

{% if query.mobilityOptions is defined %}
    {% set ids = [] %}

    {% for entry in entries %}
        {% set valid = true %}

        {% for option in query.mobilityOptions %}
            {% if not entry.mobilityOptions.contains(option) %}
                {% set valid = false %}
            {% endif %}
        {% endfor %}

        {% if valid %}
            {% set ids = ids|merge([entry.id]) %}
        {% endif %}
    {% endfor %}

    {% set entries = craft.entries.id(ids) %}
{% endif %}