JSFiddle - React, Tailwind, and code Playground

HTML

<label class="control-label bold">Full Overhead/F&amp;A Recovery</label>
<div class="control-group" id="rblFullOver">
    <div class="controls">
        <input id="fullTrue" type="radio" name="overheadRecovery" value="True" />
        <label for="fullTrue">Yes   </label>
        <input id="fullFalse" type="radio" name="overheadRecovery" value="False" />
        <label for="fullFalse">No</label>
    </div>
</div>

<label class="control-label bold">Cost Share</label>
<div class="control-group" id="rblCostShareGroup">
    <input id="shareTrue" type="radio" name="share" value="True" />
    <label for="shareTrue">Yes   </label>
    <input id="shareFalse" type="radio" name="share" value="False" />
    <label for="shareFalse">No</label>
</div>

JavaScript

$("#rblFullOver input").change(function () {
    var shareValue = $(this).val() == "True" ? "False" : "True";
    $('input[value='+shareValue+']', '#rblCostShareGroup').prop('checked', true);
});