How do I change an HTML selected option using JavaScript?

Change

document.getElementById('personlist').getElementsByTagName('option')[11].selected = 'selected'

to

document.getElementById('personlist').value=Person_ID;

Tools as pure JavaScript code for handling Selectbox:

Graphical Understanding:

Image - A

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Image - B

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Image - C

Updated - 25-June-2019 | Fiddler DEMO

JavaScript Code:

/**
 * Empty Select Box
 * @param eid Element ID
 * @param value text
 * @param text text
 * @author Neeraj.Singh
 */
function emptySelectBoxById(eid, value, text) {
    document.getElementById(eid).innerHTML = "<option value='" + value + "'>" + text + "</option>";
}


/**
 * Reset Select Box
 * @param eid Element ID
 */

function resetSelectBoxById(eid) {
    document.getElementById(eid).options[0].selected = 'selected';
}


/**
 * Set Select Box Selection By Index
 * @param eid Element ID
 * @param eindx Element Index
 */

function setSelectBoxByIndex(eid, eindx) {
    document.getElementById(eid).getElementsByTagName('option')[eindx].selected = 'selected';
    //or
    document.getElementById(eid).options[eindx].selected = 'selected';
}


/**
 * Set Select Box Selection By Value
 * @param eid Element ID
 * @param eval Element Index
 */
function setSelectBoxByValue(eid, eval) {
    document.getElementById(eid).value = eval;
}


/**
 * Set Select Box Selection By Text
 * @param eid Element ID
 * @param eval Element Index
 */
function setSelectBoxByText(eid, etxt) {
    var eid = document.getElementById(eid);
    for (var i = 0; i < eid.options.length; ++i) {
        if (eid.options[i].text === etxt)
            eid.options[i].selected = true;
    }
}


/**
 * Get Select Box Text By ID
 * @param eid Element ID
 * @return string
 */

function getSelectBoxText(eid) {
    return document.getElementById(eid).options[document.getElementById(eid).selectedIndex].text;
}


/**
 * Get Select Box Value By ID
 * @param eid Element ID
 * @return string
 */

function getSelectBoxValue(id) {
    return document.getElementById(id).options[document.getElementById(id).selectedIndex].value;
}

I believe that the blog post JavaScript Beginners – Select a dropdown option by value might help you.

<a href="javascript:void(0);" onclick="selectItemByValue(document.getElementById('personlist'),11)">change</a>

function selectItemByValue(elmnt, value){

  for(var i=0; i < elmnt.options.length; i++)
  {
    if(elmnt.options[i].value === value) {
      elmnt.selectedIndex = i;
      break;
    }
  }
}