Uncheck a checkbox with conditions

I would like to make a survey on a website with a question and three possible answers.

The problem is that i'm having trouble with the check/uncheck, I want to have only one answer checked, so if the user clicks on an answer and he has already checked an other one, it keeps only the last one.

Here is what I've done :

$("input:checkbox").click(function() {
    if($(this).is(':checked')){
        var iSurveyId = $(this).closest('div').attr('name');
        var iAnswerId = $(this).closest('p').attr('value');
        var bIsChecked = 'true';

If the user click on a checkbox, I'll get the survey ID that is in the name of my div and the ID of my answer which is in my paragraph's name.

I'm using jQuery 1.1.12 so I can't use every function for exemple I can't use .prop().