How do I change the background of the selected item in the ListBox?

You can change the colors in your ListBox’s resources, as follows:

[XAML]
<ListBox>
            <ListBox.Resources>
                <SolidColorBrush x:Key='{x:Static SystemColors.HighlightBrushKey}' Color='White'/>
                <SolidColorBrush x:Key='{x:Static SystemColors.HighlightTextBrushKey}' Color='Black'/>
                <SolidColorBrush x:Key='{x:Static SystemColors.ControlBrushKey}' Color='White'/> 
            </ListBox.Resources>
</ListBox>

The 3rd color above is the gray color in which the selected item background is rendered when the listbox does not have the focus.