// Numbas version: finer_feedback_settings
{"name": "Clodagh's copy of  BS3.3 Binomial Cookies", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Clodagh's copy of  BS3.3 Binomial Cookies", "tags": ["Binomial Distribution", "binomial distribution", "Binomial distribution", "expectation", "expected number", "probabilities", "probability", "Probability", "rebelmaths", "sc", "standard deviation", "statistical distributions", "statistics"], "metadata": {"description": "<p>rebelmaths</p>\n<p>Application of the binomial distribution given probabilities of success of an event.</p>\n<p>Finding probabilities using the binomial distribution.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{pre} $\\var{thismany}${post}</p>\n<p>{something} $\\var{number1}$ {else}</p>\n<p>&nbsp;</p>", "advice": "<p>a)</p>\n<p>$X \\sim \\operatorname{bin}(\\var{number1},\\var{prob})$, so $n= \\var{number1},\\;\\;p=\\var{prob}$.</p>\n<p></p>\n<p>b)</p>\n<p>1. \\[ \\begin{eqnarray*}\\operatorname{P}(X = \\var{thisnumber}) &amp;=&amp; \\dbinom{\\var{number1}}{\\var{thisnumber}}\\times\\var{prob}^{\\var{thisnumber}}\\times(1-\\var{prob})^{\\var{number1-thisnumber}}\\\\&amp; =&amp; \\var{comb(number1,thisnumber)} \\times\\var{prob}^{\\var{thisnumber}}\\times\\var{1-prob}^{\\var{number1-thisnumber}}\\\\&amp;=&amp;\\var{prob1}\\end{eqnarray*} \\] to 3 decimal places.</p>\n<p>&nbsp;</p>\n<p>2.&nbsp;</p>\n<p>\\[ \\begin{eqnarray*}\\operatorname{P}(X \\leq \\var{thatnumber})&amp; =&amp; \\simplify[all,!collectNumbers]{P(X = 0) + P(X = 1) + {v}*P(X = 2)+ {v1}*P(X = 3)}\\\\&amp; =&amp; \\simplify[zeroFactor,zeroTerm,unitFactor]{{1 -prob} ^ {number1}+ {number1} *{prob} *{1 -prob} ^ {number1 -1} + {v} * ({number1} * {number1 -1}/2)* {prob} ^ 2 *( {1 -prob} ^ {number1 -2})+ {v1} * ({number1} * {number1 -1}*{number1-2}/(3*2))* {prob} ^ 3&nbsp;*( {1 -prob} ^ {number1 -3})}\\\\&amp; =&amp; \\var{prob3}\\end{eqnarray*} \\]</p>\n<p>to 3 decimal places.</p>\n<p>&nbsp;</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pre": {"name": "pre", "group": "Ungrouped variables", "definition": "' '", "description": "", "templateType": "anything", "can_override": false}, "descx1": {"name": "descx1", "group": "Ungrouped variables", "definition": "\"number of chocolate chip cookies in our sample:\"", "description": "", "templateType": "anything", "can_override": false}, "tprob3c": {"name": "tprob3c", "group": "Ungrouped variables", "definition": "if(thatnumber=1,(1-prob)^number1+number1*prob*(1-prob)^(number1-1),0)", "description": "", "templateType": "anything", "can_override": false}, "tprob3b": {"name": "tprob3b", "group": "Ungrouped variables", "definition": "if(thatnumber=3,(1-prob)^number1+number1*prob*(1-prob)^(number1-1)+number1*(number1-1)*prob^2*(1-prob)^(number1-2)/2+number1*(number1-1)*(number1-2)*prob^3*(1-prob)^(number1-3)/(3*2),0)", "description": "", "templateType": "anything", "can_override": false}, "tprob3a": {"name": "tprob3a", "group": "Ungrouped variables", "definition": "if(thatnumber=2,(1-prob)^number1+number1*prob*(1-prob)^(number1-1)+number1*(number1-1)*prob^2*(1-prob)^(number1-2)/2,0)", "description": "", "templateType": "anything", "can_override": false}, "something": {"name": "something", "group": "Ungrouped variables", "definition": "''", "description": "", "templateType": "anything", "can_override": false}, "thisnumber": {"name": "thisnumber", "group": "Ungrouped variables", "definition": "if(number1<6,random(2..3), if(number1<8,random(2..4),random(3..6)))", "description": "", "templateType": "anything", "can_override": false}, "things": {"name": "things", "group": "Ungrouped variables", "definition": 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"group": "Ungrouped variables", "definition": "if(thatnumber=3,1,0)", "description": "", "templateType": "anything", "can_override": false}, "number1": {"name": "number1", "group": "Ungrouped variables", "definition": "random(5..12)*random([1,1,1,1,1,1,2,2,5])", "description": "", "templateType": "anything", "can_override": false}, "post": {"name": "post", "group": "Ungrouped variables", "definition": "\"% of biscuits made by a baker are chocolate chip cookies.\"", "description": "", "templateType": "anything", "can_override": false}, "prob2": {"name": "prob2", "group": "Ungrouped variables", "definition": "precround(tprob2,3)", "description": "", "templateType": "anything", "can_override": false}, "prob3": {"name": "prob3", "group": "Ungrouped variables", "definition": "precround(tprob3,3)", "description": "", "templateType": "anything", "can_override": false}, "prob1": {"name": "prob1", "group": "Ungrouped variables", "definition": "precround(tprob1,3)", "description": "", "templateType": "anything", "can_override": false}, "thatnumber": {"name": "thatnumber", "group": "Ungrouped variables", "definition": "random(1,2,3)", "description": "", "templateType": "anything", "can_override": false}, "thismany": {"name": "thismany", "group": "Ungrouped variables", "definition": "random(8..43)", "description": "", "templateType": "anything", "can_override": false}, "this": {"name": "this", "group": "Ungrouped variables", "definition": "\"our selection contains exactly \"", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "if(thatnumber=1,0,1)", "description": "", "templateType": "anything", "can_override": false}, "tprob1": {"name": "tprob1", "group": "Ungrouped variables", "definition": "comb(number1,thisnumber)*prob^thisnumber*(1-prob)^(number1-thisnumber)", "description": "", "templateType": "anything", "can_override": false}, "tprob3": {"name": "tprob3", "group": "Ungrouped 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{}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Assuming a binomial distribution for {descX}, write down the values of $n$ and $p$.</p>\n<p>$n=\\; $[[0]] &nbsp; &nbsp; &nbsp; &nbsp;$p=\\;$[[1]]</p>\n<p></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, 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