Try this in your code...place you all the control inside the ContentTemplate which are invoking the event and register them into the triger
<asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>
<asp:UpdatePanel ID="UpdatePanel1" runat="server">
<ContentTemplate>
<asp:Button runat="server" ID="update_Button" Text="Generate Random Number" Width="187px"
OnClick="update_Button_Click" />
<pre></ContentTemplate>
</asp:UpdatePanel>
<Triggers>
<asp:AsyncPostBackTrigger ControlID="update_Button" EventName="Click" />
</Triggers>