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{"name": "Identify independent events", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Identify independent events", "type": "question", "tags": ["Coin", "coin", "dependent", "independence", "Independence", "independent", "Probability", "probability", "random outcomes"], "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"no_flips": {"description": "<p>Number of flips of the coin</p>", "name": "no_flips", "definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables"}}, "extensions": [], "statement": "", "variable_groups": [], "parts": [{"matrix": ["1", "-1", "-1"], "displayColumns": 0, "minMarks": 0, "distractors": ["", "", ""], "variableReplacementStrategy": "originalfirst", "maxAnswers": "3", "displayType": "checkbox", "choices": ["<p>Rolling a $4$ on a die&nbsp;given that&nbsp;the previous $5$ rolls have all landed on a $6$.</p>", "<p>Randomly removing&nbsp;a king card from a standard deck of cards&nbsp;given that&nbsp;one king card has already been removed from the deck. &nbsp;</p>", "<p>Randomly&nbsp;removing a boy from a class&nbsp;that&nbsp;initially consisted of&nbsp;$15$ boys and $15$ girls given that the previous randomly&nbsp;removed student from the class was a girl.</p>"], "showFeedbackIcon": true, "prompt": "<p>Which of the following are examples of independent events?</p>", "shuffleChoices": true, "scripts": {}, "variableReplacements": [], "marks": 0, "minAnswers": "1", "warningType": "prevent", "showCorrectAnswer": true, "maxMarks": "1", "type": "m_n_2"}], "ungrouped_variables": ["no_flips"], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>This question assesses the students understanding of what it means for two events to be independent or dependent. Specifically, if two events are independent then the outcomes of one event do not affect the outcomes of the other event.</p>"}, "preamble": {"css": "", "js": ""}, "functions": {}, "advice": "<h4></h4>\n<p><span style=\"text-decoration: underline;\"><strong>Rolling a 4 on a die&nbsp;given that&nbsp;the previous 5 rolls have all landed on a 6.</strong></span></p>\n<p>Each roll of a die is independent from&nbsp;all previous rolls - the&nbsp;outcome of one roll does not change the likelihood of getting any particular score&nbsp;on the next roll.</p>\n<p>Therefore these events are independent.</p>\n<p><span style=\"text-decoration: underline;\"><strong>Randomly removing&nbsp;a King card from a standard deck of cards&nbsp;given that&nbsp;one card has already been removed from the deck. &nbsp;</strong></span></p>\n<p>The probability of removing a King from the deck depends on whether the&nbsp;first card removed was also a King.</p>\n<p>If the first card was a King, then only three Kings are left. If it wasn't a King, then there are still four Kings&nbsp;in the deck.</p>\n<p>So the probability of picking a King is&nbsp;<strong>not</strong> independent of the previous card removed.</p>\n<p><span style=\"text-decoration: underline;\"><strong>Randomly&nbsp;removing a boy from a class&nbsp;that&nbsp;initially consisted of&nbsp;15 boys and 15 girls given that the previous randomly&nbsp;removed student from the class was a girl.</strong></span></p>\n<p style=\"text-align: left;\">We are told that the class consists of $15$ boys and $15$ girls.</p>\n<p style=\"text-align: left;\">So the probability that a randomly removed student from the class is a boy is initially</p>\n<p style=\"text-align: left;\">\\[\\displaystyle\\frac{15}{30} = \\displaystyle\\frac{1}{2}.\\]</p>\n<p style=\"text-align: left;\">If we randomly withdraw one student from the class and this student is a girl, then this means that there are now $15$ boys and $14$ girls in the class.</p>\n<p style=\"text-align: left;\">As there are now fewer students in the class, the probability of randomly&nbsp;removing a boy from the class will change, meaning that these events are not independent.&nbsp;</p>\n<p style=\"text-align: left;\">In fact,&nbsp;if we now randomly withdraw another student from the class, the probability that this student is a boy is now $\\displaystyle\\frac{15}{29}$.</p>\n<p style=\"text-align: left;\">Hence&nbsp;the fact that the first randomly removed student is a girl&nbsp;causes the probability of the next randomly&nbsp;removed student being a boy to increase.</p>", "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/"}]}