checkbox

bool _value = false;
String cartype = '1';

@override
void initState() {
    cartype == "1" ? _value = true : _value = false;
    super.initState();
}

...

Checkbox(
  value: _value,
  onChanged: (bool value) {
    setState(() {
      _value = value;
    });
  },
),
Text(_value ? "a" : 'b'),