This can be added as a basic hook –
function what-ever-youwantto-callthis() {
$subRole = get_role( 'subscriber' ); //change the name of the user here
$subRole->add_cap( 'read_private_posts' ); //allows the above to read posts
$subRole->add_cap( 'read_private_pages' ); //allows the above to read pages
}
add_action( 'init', 'what-ever-youwantto-callthis' );