How to show the checked items in my CheckBox

I'm trying to have a ListBox show the checked items in a CheckBox, but it doesn't show anything. My CheckBox is under another ListBox called "listBox_Mirror". I specified it as the ElementName. Here are my codes:

StateList.cs

using System.Collections.ObjectModel;

namespace CheckedListBox
{
    public class StateList
    {
        public ObservableCollection<string> Data { get; }
        public StateList()
        {
            Data = new ObservableCollection<string>();
            Data.Add("California");
            Data.Add("Illinoi");
            Data.Add("Michigan");
            Data.Add("New York");
        }
    }
}

MainWindow.xaml

<Window x:Class="CheckedListBox.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    xmlns:local="clr-namespace:CheckedListBox"
    mc:Ignorable="d"
    Title="MainWindow" Height="500" Width="400">
<Grid>
    <ListBox ItemsSource="{Binding Path=Data}" x:Name="listBox" Margin="100,50,100,300" SelectionMode="Multiple"/>
    <ListBox ItemsSource="{Binding SelectedItems, ElementName=listBox}" x:Name="listBox_Mirror" Margin="100,200,100,150">
        <ListBox.ItemContainerStyle>
            <Style TargetType="ListBoxItem">
                <Setter Property="Template">
                    <Setter.Value>
                        <ControlTemplate TargetType="ListBoxItem">
                            <CheckBox Content="{TemplateBinding Content}"/>
                        </ControlTemplate>
                    </Setter.Value>
                </Setter>
            </Style>
        </ListBox.ItemContainerStyle>
    </ListBox>
    <ListBox ItemsSource="{Binding SelectedItems, ElementName=listBox_Mirror}" Margin="100,350,100,25"/>
</Grid>

MainWindow.xaml.cs

using System.Windows;

    namespace CheckedListBox
    {
        public partial class MainWindow : Window
        {
            public MainWindow()
            {
                InitializeComponent();
                this.DataContext = new StateList();
            }
        }
    }

Procedure: 1. Select all four items in the 1st ListBox. 2. Check the first two items (California and Illioni) in the CheckBox. 3. See if California and Illioni are shown in the 2nd ListBox. (In my case, nothing is shown.)

... I've changed the Binding property based on the IntelliSense's suggestion, but it doesn't work, too. Please tell me how to fix this. Thank you.