Hi Alok, thank you for your response. I tried updating code based on your suggestion of jquery but its not working. Below is the updated code. Can you please point out what I`m doing wrong?
 

<apex:page standardController="Opportunity" sidebar="false">

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.js" />
<script src="/soap/ajax/15.0/connection.js" type="text/javascript"></script>
<script src="/soap/ajax/15.0/apex.js" type="text/javascript"></script>
 
<script>
sforce.connection.sessionId = "{!$Api.Session_ID}";
 
function processChange(){
 
var obj = document.getElementById('{!$Component.frm.stageFieldId}');
var p = document.getElementById('{!$Component.frm.probabilityFieldId}');
 
var qr = sforce.connection.query("Select DefaultProbability From OpportunityStage where MasterLabel = '" + $(obj).val() + "'") ; 
records = qr.getArray("records");
 
for (var i=0; i< records.length; i++) {
var record = records[i];
$(p).val(record.DefaultProbability);
break;
}
return true;
}
</script>


    <apex:sectionHeader title="Edit Opportunity" subtitle="{!opportunity.name}"/>
    <apex:form id="frm">
        <apex:pageBlock title="Edit Opportunity" id="thePageBlock" mode="edit">
            <apex:pageMessages />
            <apex:pageBlockButtons >
                <apex:commandButton value="Save" action="{!save}"/>
                <apex:commandButton value="Cancel" action="{!cancel}"/>                
            </apex:pageBlockButtons>
            <apex:actionRegion >
                <apex:pageBlockSection title="Basic Information" columns="1">
                    <apex:inputField value="{!opportunity.name}"/>
                    <apex:pageBlockSectionItem >
                        <apex:outputLabel value="Stage"/>
                        <apex:outputPanel >
                            <apex:inputField value="{!opportunity.stageName}" onchange="processChange()" id="stageFieldId">
                                <apex:actionSupport event="onchange" rerender="thePageBlock"
                                                    status="status"/>
                            </apex:inputField>
                            <apex:actionStatus startText="applying value..." id="status"/>
                        </apex:outputPanel>
                    </apex:pageBlockSectionItem>
                    <apex:inputField value="{!opportunity.amount}"/>
                    <apex:inputField value="{!opportunity.closedate}"/>
                    <apex:inputField value="{!opportunity.Probability}" id="probabilityFieldId"/>

                </apex:pageBlockSection>
            </apex:actionRegion>
            <apex:pageBlockSection title="Closed Lost Information" columns="1"
                                   rendered="{!opportunity.stageName == 'Closed Lost'}">
                <apex:inputField value="{!opportunity.Primary_Competitor__c}"  required="true"/>
                <apex:inputField value="{!opportunity.Reason_Lost__c}"/>
                <apex:inputField value="{!opportunity.OrderNumber__c}"/>
                <apex:inputField value="{!opportunity.TrackingNumber__c}"/>
                
            </apex:pageBlockSection>
            
            

        </apex:pageBlock>

    </apex:form>
    
</apex:page>