diff --git a/lib/questionlib.php b/lib/questionlib.php
index 75df7ac24de60..904975f9fd064 100644
--- a/lib/questionlib.php
+++ b/lib/questionlib.php
@@ -1030,6 +1030,23 @@ function question_get_top_category($contextid, $create = false) {
     return $category;
 }
 
+/**
+ * Gets the list of top categories in the given contexts in the array("categoryid,categorycontextid") format.
+ *
+ * @param array $contextids List of context ids
+ * @return array
+ */
+function question_get_top_categories_for_contexts($contextids) {
+    global $DB;
+
+    $concatsql = $DB->sql_concat_join("','", ['id', 'contextid']);
+    list($insql, $params) = $DB->get_in_or_equal($contextids);
+    $sql = "SELECT $concatsql FROM {question_categories} WHERE contextid $insql AND parent = 0";
+    $topcategories = $DB->get_fieldset_sql($sql, $params);
+
+    return $topcategories;
+}
+
 /**
  * Gets the default category in the most specific context.
  * If no categories exist yet then default ones are created in all contexts.
diff --git a/mod/quiz/addrandom.php b/mod/quiz/addrandom.php
index 658ecb86cf2d3..144fe2e49096a 100644
--- a/mod/quiz/addrandom.php
+++ b/mod/quiz/addrandom.php
@@ -85,6 +85,10 @@
     if (!empty($data->existingcategory)) {
         list($categoryid) = explode(',', $data->category);
         $includesubcategories = !empty($data->includesubcategories);
+        if (!$includesubcategories) {
+            // If the chosen category is a top category.
+            $includesubcategories = $DB->record_exists('question_categories', ['id' => $categoryid, 'parent' => 0]);
+        }
         $returnurl->param('cat', $data->category);
 
     } else if (!empty($data->newcategory)) {
diff --git a/mod/quiz/addrandomform.php b/mod/quiz/addrandomform.php
index f66832e4b28ea..7405ddae66615 100644
--- a/mod/quiz/addrandomform.php
+++ b/mod/quiz/addrandomform.php
@@ -37,7 +37,6 @@
 class quiz_add_random_form extends moodleform {
 
     protected function definition() {
-        global $CFG, $DB;
         $mform =& $this->_form;
         $mform->setDisableShortforms();
 
@@ -49,11 +48,14 @@ protected function definition() {
                 get_string('randomfromexistingcategory', 'quiz'));
 
         $mform->addElement('questioncategory', 'category', get_string('category'),
-                array('contexts' => $usablecontexts, 'top' => false));
+                array('contexts' => $usablecontexts, 'top' => true));
         $mform->setDefault('category', $this->_customdata['cat']);
 
         $mform->addElement('checkbox', 'includesubcategories', '', get_string('recurse', 'quiz'));
 
+        $tops = question_get_top_categories_for_contexts(array_column($contexts->all(), 'id'));
+        $mform->hideIf('includesubcategories', 'category', 'in', $tops);
+
         $mform->addElement('select', 'numbertoadd', get_string('randomnumber', 'quiz'),
                 $this->get_number_of_questions_to_add_choices());
 
diff --git a/question/type/random/edit_random_form.php b/question/type/random/edit_random_form.php
index 6f771a0aee756..b2c2f2694e821 100644
--- a/question/type/random/edit_random_form.php
+++ b/question/type/random/edit_random_form.php
@@ -48,11 +48,14 @@ protected function definition() {
         $mform->addElement('header', 'generalheader', get_string("general", 'form'));
 
         $mform->addElement('questioncategory', 'category', get_string('category', 'question'),
-                array('contexts' => $this->contexts->having_cap('moodle/question:useall')));
+                array('contexts' => $this->contexts->having_cap('moodle/question:useall'), 'top' => true));
 
         $mform->addElement('advcheckbox', 'questiontext[text]',
                 get_string('includingsubcategories', 'qtype_random'), null, null, array(0, 1));
 
+        $tops = question_get_top_categories_for_contexts(array_column($this->contexts->all(), 'id'));
+        $mform->hideIf('questiontext[text]', 'category', 'in', $tops);
+
         $mform->addElement('hidden', 'qtype');
         $mform->setType('qtype', PARAM_ALPHA);
 
diff --git a/question/type/random/lang/en/qtype_random.php b/question/type/random/lang/en/qtype_random.php
index 0e15605c38f80..4c16d912cc393 100644
--- a/question/type/random/lang/en/qtype_random.php
+++ b/question/type/random/lang/en/qtype_random.php
@@ -29,6 +29,11 @@
 $string['pluginname_help'] = 'A random question is not a question type as such, but is a way of inserting a randomly-chosen question from a specified category into an activity.';
 $string['pluginnameediting'] = 'Editing a random question';
 $string['randomqname'] = 'Random ({$a})';
+$string['randomqnamefromtop'] = 'Faulty random question! Please delete this question.';
 $string['randomqplusname'] = 'Random ({$a} and subcategories)';
+$string['randomqplusnamecourse'] = 'Random (Any category in this course)';
+$string['randomqplusnamecoursecat'] = 'Random (Any category inside course category {$a})';
+$string['randomqplusnamemodule'] = 'Random (Any category of this quiz)';
+$string['randomqplusnamesystem'] = 'Random (Any system-level category)';
 $string['selectedby'] = '{$a->questionname} selected by {$a->randomname}';
 $string['selectmanualquestions'] = 'Random questions can use manually graded questions';
diff --git a/question/type/random/questiontype.php b/question/type/random/questiontype.php
index 107e647acd1a2..aecdaf6f6da75 100644
--- a/question/type/random/questiontype.php
+++ b/question/type/random/questiontype.php
@@ -127,12 +127,36 @@ public function get_question_options($question) {
      * @return string the name this question should have.
      */
     public function question_name($category, $includesubcategories) {
-        if ($includesubcategories) {
-            $string = 'randomqplusname';
+        if ($category->parent && $includesubcategories) {
+            $name = get_string('randomqplusname', 'qtype_random', shorten_text($category->name, 100));
+        } else if ($category->parent) {
+            $name = get_string('randomqname', 'qtype_random', shorten_text($category->name, 100));
+        } else if ($includesubcategories) {
+            $context = context::instance_by_id($category->contextid);
+
+            switch ($context->contextlevel) {
+                case CONTEXT_MODULE:
+                    $name = get_string('randomqplusnamemodule', 'qtype_random');
+                    break;
+                case CONTEXT_COURSE:
+                    $name = get_string('randomqplusnamecourse', 'qtype_random');
+                    break;
+                case CONTEXT_COURSECAT:
+                    $name = get_string('randomqplusnamecoursecat', 'qtype_random',
+                            shorten_text($context->get_context_name(false), 100));
+                    break;
+                case CONTEXT_SYSTEM:
+                    $name = get_string('randomqplusnamesystem', 'qtype_random');
+                    break;
+                default: // Impossible.
+                    $name = '';
+            }
         } else {
-            $string = 'randomqname';
+            // No question will ever be selected. So, let's warn the teacher.
+            $name = get_string('randomqnamefromtop', 'qtype_random');
         }
-        return get_string($string, 'qtype_random', shorten_text($category->name, 100));
+
+        return $name;
     }
 
     protected function set_selected_question_name($question, $randomname) {
@@ -143,11 +167,17 @@ protected function set_selected_question_name($question, $randomname) {
     }
 
     public function save_question($question, $form) {
+        global $DB;
+
         $form->name = '';
+        list($category) = explode(',', $form->category);
 
         // In case someone set the question text to true/false in the old style, set it properly.
         if ($form->questiontext['text']) {
             $form->questiontext['text'] = '1';
+        } else if ($DB->record_exists('question_categories', ['id' => $category, 'parent' => 0])) {
+            // The chosen category is a top category.
+            $form->questiontext['text'] = '1';
         } else {
             $form->questiontext['text'] = '0';
         }