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Probability - A Level Maths Questions\",\"description\":\"Practise 2.6 Probability A Level Maths exam-style questions with worked solutions on MathsGenie.\",\"learningResourceType\":\"Practice questions\",\"educationalLevel\":\"A Level\",\"about\":{\"@type\":\"Thing\",\"name\":\"2.6 Probability\"},\"url\":\"https://mathsgenie.co.uk/a-level/maths/ccea/probability/questions/q32\",\"inLanguage\":\"en-GB\",\"provider\":{\"@id\":\"https://mathsgenie.co.uk/#organization\"}}"}}],["$","div",null,{"className":"min-h-0 w-full flex-1 overflow-hidden bg-background","children":["$","$L3b",null,{"backHref":"/a-level/maths/ccea/questions","basePath":"/a-level/maths/ccea/probability/questions","formulaUrl":"https://ccea.org.uk/downloads/docs/Support/General/2019/Mathematical%20Formulae%20and%20Tables.pdf","initialIndex":31,"initialQuestionWindow":[{"id":"a2af0b6a-5458-47c7-8cfe-a4def00c8328","revisionId":"f7a74183-1b52-45e8-9583-6b3fb35e6489","questionNumber":null,"questionType":"LA","specification":"Events $A$ and $B$ are independent. $P(A)=p$, $P(B)=2p$ and $P(A\\cup B)=0.625$.","difficulty":null,"difficultyBand":"hard","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"49031284-524d-403b-a8ef-bf78c2043a64","label":null,"content":"Find the possible value of $p$.","markscheme":"- Uses $P(A\\cap B)=2p^2$ M1\n- Forms $p+2p-2p^2=0.625$ M1\n- Solves $2p^2-3p+0.625=0$ M1\n- $p=0.25$; the other root $1.25$ is not a valid probability A1","marks":4,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"b17f4419-4071-48ea-8de9-c2b61650d867","revisionId":"6524c106-72fc-4750-b831-9ac4d4948777","questionNumber":null,"questionType":"LA","specification":"On each of three independent days, a ferry is delayed with probability 0.15.","difficulty":null,"difficultyBand":"hard","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"457f1457-291c-4a37-8f82-9afdbf6d3056","label":"a","content":"Find the probability of at least one delay.","markscheme":"- Uses the complement $1-0.85^3$ M1\n- Probability $=0.386$ to 3 significant figures A1","marks":2,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]},{"id":"cc5b6de3-ec17-406c-999b-1291e3986432","label":"b","content":"Find the probability of exactly one delay.","markscheme":"- Uses $3(0.15)(0.85)^2$ M1\n- Probability $=0.325$ to 3 significant figures A1","marks":2,"order":1,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"bbff1ee6-fa6f-4218-bff0-e42164b52d94","revisionId":"0ab49d8f-6d84-42ea-a834-173d260ef8dd","questionNumber":null,"questionType":"LA","specification":"Machines A, B and C produce 20%, 45% and 35% of a company's components. Overall, 4% are faulty. The fault rates for A and B are 3% and 5% respectively.","difficulty":null,"difficultyBand":"hard","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"0ab77525-b981-44dc-b578-27ed7d3669fb","label":null,"content":"Find the percentage of components from C that are faulty.","markscheme":"- Let the fault probability for C be $p$ and uses $0.04=0.20(0.03)+0.45(0.05)+0.35p$ M1\n- Known contributions total $0.006+0.0225=0.0285$ M1\n- $0.35p=0.0115$, so $p=0.032857\\ldots$ M1\n- Percentage $=3.29\\%$ to 3 significant figures 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Probability","topicId":"712e3768-c7f1-4828-9533-c640dcaf6db9","topicSidebar":"$L3c","topicSlug":"probability","topicTitle":"2.6 Probability"}]}],"$L3d","$L3e"]}]

2.6 Probability

Question 7

2.6 Probability Questions

2.6 Probability

Question 7

2.6 Probability Questions