In my VisualForce page, if I have more than one apex:actionSupport event="onchange" then the event doesn't fire until a second input component is accessed.  If there is one then it fires immdiately.  If there anyway to make event fire everytime?

VF Code:
<apex:page controller="TextApex" >
<apex:form >
<apex:pageBlock >

<apex:selectRadio id="slctRd" dir="ltr" required="true" layout="pageDirection" value="{!selectedValue}" immediate="true">
<apex:actionSupport event="onchange" action="{!MethodOne}" reRender="test"/>
<apex:selectOptions id="selRdOptn" value="{!Options}"/>
</apex:selectRadio>

<apex:selectRadio id="slctRd1" dir="ltr" required="true" layout="pageDirection" value="{!selectedValue1}" immediate="true">
<apex:actionSupport event="onchange" action="{!MethodTwo}" reRender="test1"/>
<apex:selectOptions id="selRdOptn1" value="{!Options1}"/>
</apex:selectRadio>

<apex:outputText id="test" value="{!test}"></apex:outputText><br/>
<apex:outputText id="test1" value="{!test1}"></apex:outputText>

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

Apex:
public class TextApex {

    public String selectedValue {get; set;}
    public List<SelectOption> Options {get; set;}
    public String test {get;set;}
    
    public String selectedValue1 {get; set;}
    public List<SelectOption> Options1 {get; set;}
    public String test1 {get;set;} 
       
    public TextApex() {
        Options = new List<SelectOption>();
        Options.add(new SelectOption('test1', 'test1'));
        Options.add(new SelectOption('test2', 'test2'));

        Options1 = new List<SelectOption>();
        Options1.add(new SelectOption('test3', 'test3'));
        Options1.add(new SelectOption('test4', 'test4'));
    }
    
   public void MethodOne() { test = 'Hello World' + selectedValue ; }
   public void MethodTwo() { test1 = 'Hello World' + selectedValue1 ; }
}