Index: class-wp-posts-list-table.php
===================================================================
--- class-wp-posts-list-table.php	(revision 37665)
+++ class-wp-posts-list-table.php	(working copy)
@@ -799,7 +799,7 @@
 	 * @param WP_Post $post The current WP_Post object.
 	 */
 	public function column_cb( $post ) {
-		if ( current_user_can( 'edit_post', $post->ID ) ): ?>
+		if ( current_user_can( 'edit_post', $post->ID ) || current_user_can( 'delete_post', $post->ID ) ): ?>
 			<label class="screen-reader-text" for="cb-select-<?php the_ID(); ?>"><?php
 				printf( __( 'Select %s' ), _draft_or_post_title() );
 			?></label>