How to change the background-color of jumbrotron?

Try this:

<div style="background:transparent !important" class="jumbotron">
    <h1>Welcome!</h1>
    <p>We're an awesome company that creates virtual things for portable devices.</p>
    <p><a class="btn btn-primary btn-lg" role="button">Learn more</a></p>
</div>

Inline CSS gets preference over classes defined in a .css file and the classes declared inside <style>