Use jQuery to change a second select list based on the first select list option

Answer 1

Store all #select2's options in a variable, filter them according to the value of the chosen option in #select1, and set them using .html() in #select2:

var $select1 = $( '#select1' ),
    $select2 = $( '#select2' ),
    $options = $select2.find( 'option' );

$select1.on('change', function() {
    $select2.html($options.filter('[value="' + this.value + '"]'));
}).trigger('change'); 

Here's a fiddle