// Numbas version: exam_results_page_options
{"name": "Julie's copy of Select a card and roll a dice", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": ["Probability", "probability", "rebel", "Rebel", "REBEL", "rebelmaths"], "statement": "<p><strong>Please give your answers to 3 decimal places.</strong></p>\n<p>A student selects one card at random from a pack of 52 playing cards and then rolls a dice once.</p>\n<p>Let event $A$ be that the card she picks is a $\\var{suit}$.</p>\n<p>Let event $B$ be that the number she rolls is greater than $\\var{n}$.</p>", "parts": [{"prompt": "<p>Calculate the probability that the card she picks is a $\\var{suit}$ and the number she rolls is greater than $\\var{n}$.</p>", "maxValue": "(1/4)*((6-n)/6)", "variableReplacements": [], "showPrecisionHint": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "minValue": "(1/4)*((6-n)/6)", "allowFractions": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "type": "numberentry", "precision": "3", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision."}, {"prompt": "<p>Calculate the probability that neither of these two events will occur.</p>", "maxValue": "(3/4)*(n/6)", "variableReplacements": [], "showPrecisionHint": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "minValue": "(3/4)*(n/6)", "allowFractions": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "type": "numberentry", "precision": "3", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision."}, {"prompt": "<p>Calculate the probability that only one of these two events will occur.</p>", "maxValue": "(1/4)*(n/6)+(3/4)*((6-n)/6)", "variableReplacements": [], "showPrecisionHint": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "minValue": "(1/4)*(n/6)+(3/4)*((6-n)/6)", "allowFractions": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "type": "numberentry", "precision": "3", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision."}, {"prompt": "<p>What is the probability that at least one of these two events will occur?</p>", "maxValue": "(1/4)*(n/6)+(3/4)*((6-n)/6)+(1/4)*((6-n)/6)", "variableReplacements": [], "showPrecisionHint": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "minValue": "(1/4)*(n/6)+(3/4)*((6-n)/6)+(1/4)*((6-n)/6)", "allowFractions": false, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": "0", "type": "numberentry", "precision": "3", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision."}], "metadata": {"description": "<p>A student selects a card from a deck of 52 and rolls a dice once.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"suit": {"description": "<p>suit</p>", "name": "suit", "group": "Ungrouped variables", "templateType": "anything", "definition": "random ('diamond','spade','heart','club')"}, "n": {"description": "<p>number on dice is greater than n.</p>", "name": "n", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..4)"}}, "name": "Julie's copy of Select a card and roll a dice", "advice": "<p>The outcome of selecting the card is&nbsp;<strong>independent</strong>&nbsp;of (not effected by) the outcome of rolling the dice.</p>\n<p>If two events, $A$ and $B$, are independent then $P(A\\cap B)=P(A)\\times P(B)$.</p>\n<p><strong>Part a)</strong></p>\n<address></address>\n<p>Let $A$ represent the event that a $\\var{suit}$ is selected and let $B$ represent the event that a number greater than $\\var{n}$ is rolled.</p>\n<p>&nbsp;$P(A)$ is $\\frac{13}{52}=\\frac{1}{4}$ and $P(B)$ is &nbsp;$\\frac{\\var{6-n}}{6}$.</p>\n<p>Therefore the probability of drawing a $\\var{suit}$ and rolling a number greater than $\\var{n}$ is $ P(A) \\times P(B)=\\frac{1}{4} \\times \\frac{\\var{6-n}}{6}$.&nbsp;</p>\n<p><strong>Part b)</strong></p>\n<p></p>\n<p>The probability that neither of these events occur is the probability of not drawing a $\\var{suit}$ which is $P(A^c)=\\frac{3}{4}$ mulitiplied by the probability of not rolling a number greater than $\\var{n}$ which is&nbsp;$P(B^c)=\\frac{\\var{n}}{6}$&nbsp;.</p>\n<p><strong>Part c)</strong></p>\n<p>The probability that only one of these events occur is $P(A ^c\\cap B)+P(A \\cap B^c)=(\\frac{3}{4} \\times \\frac{\\var{6-n}}{6})+(\\frac{1}{4} \\times \\frac{\\var{n}}{6})$.</p>\n<p><strong>Part d)</strong></p>\n<p>The probability &nbsp;that at least one of these two events will occur is $1- P$(neither of the events occur)$=1-(P(A^c)\\times P(B^c))= 1-(\\frac{3}{4}\\times \\frac{\\var{n}}{6})$</p>", "functions": {}, "extensions": [], "ungrouped_variables": ["n", "suit"], "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}