Binding SelectedItem to IsChecked - powershell

Question

I have listBox modified for check boxes. I would like to bind the selectedItem to the check so that I can use $WPFlbSiteList.SelectedItem as the basis of selecting items that are checked.
Basically, I have generated a list I need the checks to equate to the selected item. This selected item also needs to work in a multi selection capacity rather than one at a time.
<ListBox x:Name="lbSiteList" SelectionMode="MultiExtended" Margin="355,45,411,1014" ItemsSource="{Binding .}">
<ListBox.ItemTemplate>
<DataTemplate>
<CheckBox Content="{Binding .}" IsChecked="{Binding RelativeSource={RelativeSource AncestorType={x:Type ListBoxItem}}, Path=IsSelected}" Margin="2,2,0,0"/>
</DataTemplate>
</ListBox.ItemTemplate>
</ListBox>
My function to write to the console which of my checked items are selected.
$WPFbtnUpdate.Add_Click({
#List the sites that are ticked
foreach ($WPFlbSiteList.Items in $WPFlbSiteList){
$x=$WPFlbSiteList.SelectedItems
write-host $x
}
})

Answer 1

As noted in the comments you can bind the checkbox IsChecked value to IsSelected of it's relative ancestor (the listbox) with:
<CheckBox IsChecked="{Binding RelativeSource={RelativeSource AncestorType={x:Type ListBoxItem}}, Path=IsSelected" />
Your real issue, however, seems to be that you're using an invalid value for the ListBox' SelectionMode property.
In WPF, the valid selection modes are:
Extended - The user can select multiple consecutive items while holding down the SHIFT key.
Multiple - The user can select multiple items without holding down a modifier key.
Single - The user can select only one item at a time.