Sounds straight forward. Try out.
Either put both the controls in update panel and just handle the first radio buttonlist selectedindex change in code behind. OR keep second radio button in Update panel having first radio button control's selectedindexchange as a async trigger. Rest all will be automatically handled by AJAX controls.
To have some knowledge on UpdatePanel in case needed:
Here you go:
UpdatePanel Control Overview[
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UpdatePanel control[
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UpdatePanel Class[
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