// Numbas version: finer_feedback_settings
{"name": "Probabilities of certain and impossible events", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Determine whether outcomes are impossible or certain to occur.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["dice", "students"], "type": "question", "extensions": [], "advice": "<h4>a)</h4>\n<p>We are told that a fair, $6$-sided die is thrown.</p>\n<p>The sides on a fair, $6$-sided die are numbered $1$ to $6$.&nbsp;There is <strong>no</strong>&nbsp;$7$ on such a die.</p>\n<p>Therefore, there is <strong>no</strong> chance of the die landing on a $7$, which means that the probability of the die landing on a $7$&nbsp;<strong>must</strong> be $0$.</p>\n<p>Hence, this is an <strong>impossible</strong> event.</p>\n<h4>b)</h4>\n<p>We are told that a teacher chooses a student at random from a class of $20$ girls.</p>\n<p>The key piece of information to notice here is that the teacher's class is comprised of $20$ <strong>girls</strong>.&nbsp;Everybody in the class is a girl.</p>\n<p>Therefore, the student that the teacher randomly chooses from the class <strong>must</strong> be a girl, which means that the probability that the student chosen is a girl is $1$.</p>\n<p>Hence, this is a <strong>certain</strong> event.</p>", "variable_groups": [], "rulesets": {}, "statement": "<p>Probability is the chance that an event will occur.</p>\n<p>A certain event is an event that will definitely happen and&nbsp;therefore has a probability of $1$.</p>\n<p>An impossible&nbsp;event is an event that will never happen and therefore has a probability of $0$.&nbsp;</p>", "name": "Probabilities of certain and impossible events", "parts": [{"scripts": {}, "gaps": [{"shuffleChoices": false, "type": "1_n_2", "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 0, "showFeedbackIcon": true, "choices": ["<p>1</p>", "<p>1/2</p>", "<p>1/6</p>", "<p>0</p>"], "scripts": {}, "distractors": ["", "", "", ""], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "matrix": ["0", "0", 0, "1"], "displayType": "dropdownlist"}, {"shuffleChoices": true, "type": "1_n_2", "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 0, "showFeedbackIcon": true, "choices": ["<p>impossible</p>", "<p>certain</p>", "<p>unlikely</p>"], "scripts": {}, "distractors": ["", "", ""], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "matrix": ["1", 0, 0], "displayType": "dropdownlist"}], "type": "gapfill", "showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>A fair $6$-sided die is rolled. The probability that the die lands on a $\\var{dice}$ is [[0]]. Therefore, we say that this event is [[1]].</p>\n<p></p>", "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "gaps": [{"shuffleChoices": false, "type": "1_n_2", "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 0, "showFeedbackIcon": true, "choices": ["<p>1</p>", "<p>{students-1}/{students}</p>", "<p>1/{students}</p>", "<p>0</p>"], "scripts": {}, "distractors": ["", "", "", ""], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "matrix": ["1", 0, 0, "0"], "displayType": "dropdownlist"}, {"shuffleChoices": true, "type": "1_n_2", "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 0, "showFeedbackIcon": true, "choices": ["<p>certain</p>", "<p>impossible</p>", "<p>unlikely</p>"], "scripts": {}, "distractors": ["", "", ""], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "matrix": ["1", 0, 0], "displayType": "dropdownlist"}], "type": "gapfill", "showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>A teacher chooses a student at random from a class of $\\var{students}$ girls.&nbsp;The probability that the student chosen is a girl is [[0]]. Therefore, we say that this event is [[1]].</p>", "variableReplacementStrategy": "originalfirst"}], "tags": ["Certain", "Chance", "event", "Impossible", "Probability", "probability", "taxonomy"], "preamble": {"css": "", "js": ""}, "functions": {}, "variables": {"dice": {"description": "", "group": "Ungrouped variables", "definition": "random(7,8,9)", "name": "dice", "templateType": "anything"}, "students": {"description": "", "group": "Ungrouped variables", "definition": "random(20..30 #5)", "name": "students", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}