WP Debug enabled Undefined index error in a widget

Whenever you use a value from an array, like $array['key'] where it’s possible that the 'key' doesn’t exist (such as the first time a widget is used) you need to check that it exists before using it or you’ll get errors on those occasions where it hasn’t been set.

Your problem is that when the widget’s first added 'tick_the_snippet_type' doesn’t exist on $instance, so you need to account for this possibility. I’d suggest creating a variable to pass to checked() which will either contain tick_the_snippet_type or a default if it doesn’t exist:

if ( isset( $instance['tick_the_snippet_type'] ) ) {
    $value = $instance['tick_the_snippet_type'];
} else {
    $value = false;
}

Which can be written on one line with a ternary operator:

$value = isset( $instance['tick_the_snippet_type'] ) ? $instance['tick_the_snippet_type'] : false;

And then use this for checked:

<?php checked( $value, 'tick_snippet_4' ); ?>