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1

HTML

<label><input type="radio" name="nomer" id="perv" value="perv">1</label>
<label><input type="radio" name="nomer" id="vtoroy" value="vtoroy">2</label>

<div id="kartinka" style="height: 200px; width: 200px;">

JavaScript

$(document).ready(function(){   
  if ($('#perv').is(':checked')) { 
           $('#kartinka').css('backgroundImage', 'url(http://images5.fanpop.com/image/photos/30800000/Nature-view-grass-30826225-1600-1200.jpg)');

  } 
  if ($('#vtoroy').is(':checked')) { 
           $('#kartinka').css('backgroundImage', 'url(http://images5.fanpop.com/image/photos/30800000/Nature-view-grass-30826225-1600-1200.jpg)');
  } 
};