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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":32,"initialQuestionWindow":[{"id":"8e070193-dd5b-456f-9bcc-1a8fabf34382","revisionId":"4a365a93-aeb0-4e90-adba-9f44ea7405c6","questionNumber":null,"questionType":"LA","specification":"","difficulty":5,"difficultyBand":"medium","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"e9fea8e6-ad28-4701-a051-f805182abd6b","label":null,"content":"In a high-precision manufacturing facility, the probabilities of three distinct system faults—Mechanical ($M$), Electrical ($E$), and Software ($S$)—occurring during a single operation are monitored. It is known that Mechanical and Software faults are mutually exclusive events ($M \\cap S = \\emptyset$). The following probabilities are recorded:\n\n\\[ P(M \\cap E') = \\frac{7}{50} \\]\n\\[ P(M \\cap E) = 0.035 \\]\n\\[ P(E \\cap M' \\cap S') = 0.245 \\]\n\\[ P(E \\cap S) = \\frac{3}{20} \\]\n\\[ P(S \\cap E') = 0.38 \\]\n\nThe probability that an operation completes without any of these three faults occurring is denoted by $\\lambda$. Determine the value of $\\lambda$.","markscheme":"- Recognises that the total probability of the sample space is 1, so the sum of the probabilities of all disjoint regions and $\\lambda$ must equal 1: $P(M \\cap E') + P(M \\cap E) + P(E \\cap M' \\cap S') + P(E \\cap S) + P(S \\cap E') + \\lambda = 1$ M1\n- Converts fractions to decimals and sums the known probabilities: $0.14 + 0.035 + 0.245 + 0.15 + 0.38 = 0.95$ A1\n- Calculates the value of the remaining region: $\\lambda = 1 - 0.95 = 0.05$ A1","marks":3,"order":0,"markingRubric":null,"tableImages":[],"explanation":{"methods":[{"id":"venndiagram","label":"Venn Diagram Representation","steps":[{"type":"text","order":0,"title":"Visualize the Venn Diagram","content":"To solve this problem, we can represent the events on a Venn diagram.\n\nWe are given that Mechanical ($M$) and Software ($S$) faults are mutually exclusive, which means they do not overlap ($M \\cap S = \\emptyset$).\n\nBoth $M$ and $S$ can intersect with Electrical faults ($E$). Therefore, our Venn diagram will consist of:\n- Two non-overlapping circles for $M$ and $S$\n- A central circle for $E$ that intersects with both $M$ and $S$"},{"type":"text","order":1,"title":"Convert probabilities to decimals","content":"First, let's convert all the given probabilities into decimal form to make our calculations consistent:\n\n- $P(M \\cap E') = \\frac{7}{50} = 0.14$\n- $P(M \\cap E) = 0.035$\n- $P(E \\cap M' \\cap S') = 0.245$\n- $P(E \\cap S) = \\frac{3}{20} = 0.15$\n- $P(S \\cap E') = 0.38$"},{"type":"text","order":2,"title":"Identify the disjoint regions","content":"Because $M$ and $S$ do not overlap, any event in our system belongs to exactly one of the following 6 disjoint (mutually exclusive) regions:\n\n1. Only Mechanical faults: $M \\cap E' = M \\cap E' \\cap S'$\n2. Mechanical and Electrical faults only: $M \\cap E = M \\cap E \\cap S'$\n3. Only Electrical faults: $E \\cap M' \\cap S'$\n4. Electrical and Software faults only: $E \\cap S = E \\cap S \\cap M'$\n5. Only Software faults: $S \\cap E' = S \\cap E' \\cap M'$\n6. No faults: This is the region outside all three circles, represented by $\\lambda$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\begin{aligned} P(\\text{any fault}) &= \\htmlData{anchor=r1}{\\color{@sky}{P(M \\cap E')}} + \\htmlData{anchor=r2}{\\color{@amber}{P(M \\cap E)}} + \\htmlData{anchor=r3}{\\color{@purple}{P(E \\cap M' \\cap S')}} \\\\ &\\quad + \\htmlData{anchor=r4}{\\color{@green}{P(E \\cap S)}} + \\htmlData{anchor=r5}{\\color{@pink}{P(S \\cap E')}} \\end{aligned}$$"},{"latex":"$$$\\begin{aligned} P(\\text{any fault}) &= \\htmlData{anchor=r1-val}{\\color{@sky}{0.14}} + \\htmlData{anchor=r2-val}{\\color{@amber}{0.035}} + \\htmlData{anchor=r3-val}{\\color{@purple}{0.245}} \\\\ &\\quad + \\htmlData{anchor=r4-val}{\\color{@green}{0.15}} + \\htmlData{anchor=r5-val}{\\color{@pink}{0.38}} \\end{aligned}$$"},{"latex":"$$$P(\\text{any fault}) = 0.95$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"r1"},{"color":"sky","style":"text-color","anchor":"r1-val"},{"color":"amber","style":"text-color","anchor":"r2"},{"color":"amber","style":"text-color","anchor":"r2-val"}],"connections":[{"to":"r1-val","from":"r1","color":"sky","label":"substitute","style":"solid"},{"to":"r2-val","from":"r2","color":"amber","label":"substitute","style":"solid"}]},"order":3,"title":"Sum the regions","description":"Summing the probabilities of these five disjoint fault-containing regions gives us the total probability of at least one fault occurring."},{"type":"text","order":4,"title":"Calculate the value of lambda","content":"The total probability of the entire sample space is $1$. Therefore, the probability $\\lambda$ of having no faults is:\n\n$$\\lambda = 1 - P(\\text{any fault})$$\n$$\\lambda = 1 - 0.95 = 0.05$$\n\nThus, the probability that an operation completes without any of these three faults occurring is **$0.05$**."}]},{"id":"algebraic","label":"Algebraic Set Formulas","steps":[{"type":"text","order":0,"title":"Analyze the given information","content":"Let's first convert all the given fractional probabilities into decimals to keep the calculations consistent:\n\n- Mechanical and Software faults are mutually exclusive: \n $$M \\cap S = \\emptyset \\implies P(M \\cap S) = 0 \\quad \\text{and} \\quad P(M \\cap E \\cap S) = 0$$\n- $P(M \\cap E') = \\frac{7}{50} = 0.14$\n- $P(M \\cap E) = 0.035$\n- $P(E \\cap M' \\cap S') = 0.245$\n- $P(E \\cap S) = \\frac{3}{20} = 0.15$\n- $P(S \\cap E') = 0.38$"},{"type":"hyper_latex","block":{"nodes":[{"text":"Since $M = (M \\cap E) \\cup (M \\cap E')$ is a union of disjoint events:"},{"latex":"$$P(M) = \\htmlData{anchor=pme}{\\color{@sky}{P(M \\cap E)}} + \\htmlData{anchor=pmep}{\\color{@amber}{P(M \\cap E')}}$"},{"latex":"$$P(M) = \\htmlData{anchor=pme-val}{\\color{@sky}{0.035}} + \\htmlData{anchor=pmep-val}{\\color{@amber}{0.14}} = 0.175$"},{"text":"Since $S = (S \\cap E) \\cup (S \\cap E')$ is also a union of disjoint events:"},{"latex":"$$P(S) = \\htmlData{anchor=pse}{\\color{@teal}{P(S \\cap E)}} + \\htmlData{anchor=psep}{\\color{@purple}{P(S \\cap E')}}$"},{"latex":"$$P(S) = \\htmlData{anchor=pse-val}{\\color{@teal}{0.15}} + \\htmlData{anchor=psep-val}{\\color{@purple}{0.38}} = 0.53$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"pme"},{"color":"sky","style":"text-color","anchor":"pme-val"},{"color":"teal","style":"text-color","anchor":"pse"},{"color":"teal","style":"text-color","anchor":"pse-val"}],"connections":[{"to":"pme-val","from":"pme","color":"sky","label":"substitute","style":"solid"},{"to":"pse-val","from":"pse","color":"teal","label":"substitute","style":"solid"}]},"order":1,"title":"Calculate individual probabilities","description":"We use the law of total probability to decompose $M$ and $S$ using their intersections with $E$ and $E'$."},{"type":"text","order":2,"title":"Calculate probability of E","content":"Because $M$ and $S$ are mutually exclusive ($M \\cap S = \\emptyset$), any event in $E$ must belong to exactly one of three mutually exclusive regions:\n\n1. Inside $M$ (which is $E \\cap M$)\n2. Inside $S$ (which is $E \\cap S$)\n3. Outside both $M$ and $S$ (which is $E \\cap M' \\cap S'$)\n\nTherefore, we can sum these three disjoint components to find $P(E)$:\n\n$$\\begin{aligned} P(E) &= P(E \\cap M) + P(E \\cap S) + P(E \\cap M' \\cap S') \\\\ &= 0.035 + 0.15 + 0.245 \\\\ &= 0.43 \\end{aligned}$$"},{"type":"text","order":3,"title":"Apply three-event addition rule","content":"Now we apply the probability addition rule for three events:\n\n$$\\begin{aligned} P(M \\cup E \\cup S) &= P(M) + P(E) + P(S) \\\\ &\\quad - P(M \\cap E) - P(E \\cap S) - P(M \\cap S) + P(M \\cap E \\cap S) \\end{aligned}$$\n\nSubstituting our known values (where $P(M \\cap S) = 0$ and $P(M \\cap E \\cap S) = 0$):\n\n$$\\begin{aligned} P(M \\cup E \\cup S) &= 0.175 + 0.43 + 0.53 - 0.035 - 0.15 - 0 + 0 \\\\ &= 0.95 \\end{aligned}$$"},{"type":"text","order":4,"title":"Determine value of lambda","content":"The probability $\\lambda$ that an operation completes without any of these three faults occurring is the complement of the union of the three events:\n\n$$\\begin{aligned} \\lambda &= P((M \\cup E \\cup S)') \\\\ &= 1 - P(M \\cup E \\cup S) \\\\ &= 1 - 0.95 \\\\ &= 0.05 \\end{aligned}$$\n\nThus, the probability that the system operates without any faults is $\\lambda = 0.05$."}]}],"generatedAt":"2026-06-09T07:30:22.630Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"e9fea8e6-ad28-4701-a051-f805182abd6b:venndiagram","label":"Venn Diagram Representation","steps":[{"type":"text","order":0,"title":"Visualize the Venn Diagram","content":"To solve this problem, we can represent the events on a Venn diagram.\n\nWe are given that Mechanical ($M$) and Software ($S$) faults are mutually exclusive, which means they do not overlap ($M \\cap S = \\emptyset$).\n\nBoth $M$ and $S$ can intersect with Electrical faults ($E$). Therefore, our Venn diagram will consist of:\n- Two non-overlapping circles for $M$ and $S$\n- A central circle for $E$ that intersects with both $M$ and $S$"},{"type":"text","order":1,"title":"Convert probabilities to decimals","content":"First, let's convert all the given probabilities into decimal form to make our calculations consistent:\n\n- $P(M \\cap E') = \\frac{7}{50} = 0.14$\n- $P(M \\cap E) = 0.035$\n- $P(E \\cap M' \\cap S') = 0.245$\n- $P(E \\cap S) = \\frac{3}{20} = 0.15$\n- $P(S \\cap E') = 0.38$"},{"type":"text","order":2,"title":"Identify the disjoint regions","content":"Because $M$ and $S$ do not overlap, any event in our system belongs to exactly one of the following 6 disjoint (mutually exclusive) regions:\n\n1. Only Mechanical faults: $M \\cap E' = M \\cap E' \\cap S'$\n2. Mechanical and Electrical faults only: $M \\cap E = M \\cap E \\cap S'$\n3. Only Electrical faults: $E \\cap M' \\cap S'$\n4. Electrical and Software faults only: $E \\cap S = E \\cap S \\cap M'$\n5. Only Software faults: $S \\cap E' = S \\cap E' \\cap M'$\n6. No faults: This is the region outside all three circles, represented by $\\lambda$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\begin{aligned} P(\\text{any fault}) &= \\htmlData{anchor=r1}{\\color{@sky}{P(M \\cap E')}} + \\htmlData{anchor=r2}{\\color{@amber}{P(M \\cap E)}} + \\htmlData{anchor=r3}{\\color{@purple}{P(E \\cap M' \\cap S')}} \\\\ &\\quad + \\htmlData{anchor=r4}{\\color{@green}{P(E \\cap S)}} + \\htmlData{anchor=r5}{\\color{@pink}{P(S \\cap E')}} \\end{aligned}$$"},{"latex":"$$$\\begin{aligned} P(\\text{any fault}) &= \\htmlData{anchor=r1-val}{\\color{@sky}{0.14}} + \\htmlData{anchor=r2-val}{\\color{@amber}{0.035}} + \\htmlData{anchor=r3-val}{\\color{@purple}{0.245}} \\\\ &\\quad + \\htmlData{anchor=r4-val}{\\color{@green}{0.15}} + \\htmlData{anchor=r5-val}{\\color{@pink}{0.38}} \\end{aligned}$$"},{"latex":"$$$P(\\text{any fault}) = 0.95$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"r1"},{"color":"sky","style":"text-color","anchor":"r1-val"},{"color":"amber","style":"text-color","anchor":"r2"},{"color":"amber","style":"text-color","anchor":"r2-val"}],"connections":[{"to":"r1-val","from":"r1","color":"sky","label":"substitute","style":"solid"},{"to":"r2-val","from":"r2","color":"amber","label":"substitute","style":"solid"}]},"order":3,"title":"Sum the regions","description":"Summing the probabilities of these five disjoint fault-containing regions gives us the total probability of at least one fault occurring."},{"type":"text","order":4,"title":"Calculate the value of lambda","content":"The total probability of the entire sample space is $1$. Therefore, the probability $\\lambda$ of having no faults is:\n\n$$\\lambda = 1 - P(\\text{any fault})$$\n$$\\lambda = 1 - 0.95 = 0.05$$\n\nThus, the probability that an operation completes without any of these three faults occurring is **$0.05$**."}]},{"id":"e9fea8e6-ad28-4701-a051-f805182abd6b:algebraic","label":"Algebraic Set Formulas","steps":[{"type":"text","order":0,"title":"Analyze the given information","content":"Let's first convert all the given fractional probabilities into decimals to keep the calculations consistent:\n\n- Mechanical and Software faults are mutually exclusive: \n $$M \\cap S = \\emptyset \\implies P(M \\cap S) = 0 \\quad \\text{and} \\quad P(M \\cap E \\cap S) = 0$$\n- $P(M \\cap E') = \\frac{7}{50} = 0.14$\n- $P(M \\cap E) = 0.035$\n- $P(E \\cap M' \\cap S') = 0.245$\n- $P(E \\cap S) = \\frac{3}{20} = 0.15$\n- $P(S \\cap E') = 0.38$"},{"type":"hyper_latex","block":{"nodes":[{"text":"Since $M = (M \\cap E) \\cup (M \\cap E')$ is a union of disjoint events:"},{"latex":"$$P(M) = \\htmlData{anchor=pme}{\\color{@sky}{P(M \\cap E)}} + \\htmlData{anchor=pmep}{\\color{@amber}{P(M \\cap E')}}$"},{"latex":"$$P(M) = \\htmlData{anchor=pme-val}{\\color{@sky}{0.035}} + \\htmlData{anchor=pmep-val}{\\color{@amber}{0.14}} = 0.175$"},{"text":"Since $S = (S \\cap E) \\cup (S \\cap E')$ is also a union of disjoint events:"},{"latex":"$$P(S) = \\htmlData{anchor=pse}{\\color{@teal}{P(S \\cap E)}} + \\htmlData{anchor=psep}{\\color{@purple}{P(S \\cap E')}}$"},{"latex":"$$P(S) = \\htmlData{anchor=pse-val}{\\color{@teal}{0.15}} + \\htmlData{anchor=psep-val}{\\color{@purple}{0.38}} = 0.53$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"pme"},{"color":"sky","style":"text-color","anchor":"pme-val"},{"color":"teal","style":"text-color","anchor":"pse"},{"color":"teal","style":"text-color","anchor":"pse-val"}],"connections":[{"to":"pme-val","from":"pme","color":"sky","label":"substitute","style":"solid"},{"to":"pse-val","from":"pse","color":"teal","label":"substitute","style":"solid"}]},"order":1,"title":"Calculate individual probabilities","description":"We use the law of total probability to decompose $M$ and $S$ using their intersections with $E$ and $E'$."},{"type":"text","order":2,"title":"Calculate probability of E","content":"Because $M$ and $S$ are mutually exclusive ($M \\cap S = \\emptyset$), any event in $E$ must belong to exactly one of three mutually exclusive regions:\n\n1. Inside $M$ (which is $E \\cap M$)\n2. Inside $S$ (which is $E \\cap S$)\n3. Outside both $M$ and $S$ (which is $E \\cap M' \\cap S'$)\n\nTherefore, we can sum these three disjoint components to find $P(E)$:\n\n$$\\begin{aligned} P(E) &= P(E \\cap M) + P(E \\cap S) + P(E \\cap M' \\cap S') \\\\ &= 0.035 + 0.15 + 0.245 \\\\ &= 0.43 \\end{aligned}$$"},{"type":"text","order":3,"title":"Apply three-event addition rule","content":"Now we apply the probability addition rule for three events:\n\n$$\\begin{aligned} P(M \\cup E \\cup S) &= P(M) + P(E) + P(S) \\\\ &\\quad - P(M \\cap E) - P(E \\cap S) - P(M \\cap S) + P(M \\cap E \\cap S) \\end{aligned}$$\n\nSubstituting our known values (where $P(M \\cap S) = 0$ and $P(M \\cap E \\cap S) = 0$):\n\n$$\\begin{aligned} P(M \\cup E \\cup S) &= 0.175 + 0.43 + 0.53 - 0.035 - 0.15 - 0 + 0 \\\\ &= 0.95 \\end{aligned}$$"},{"type":"text","order":4,"title":"Determine value of lambda","content":"The probability $\\lambda$ that an operation completes without any of these three faults occurring is the complement of the union of the three events:\n\n$$\\begin{aligned} \\lambda &= P((M \\cup E \\cup S)') \\\\ &= 1 - P(M \\cup E \\cup S) \\\\ &= 1 - 0.95 \\\\ &= 0.05 \\end{aligned}$$\n\nThus, the probability that the system operates without any faults is $\\lambda = 0.05$."}]}],"generatedAt":"2026-06-09T07:30:41.940Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":74},"walkthroughVideo":null},{"id":"b1d2f540-302d-4877-a546-a8aa49bf2a76","revisionId":"8ce15dc9-9793-4e35-8bb4-94586d7051b0","questionNumber":null,"questionType":"LA","specification":"| | Passed | Did not pass | Total |\n|---|---:|---:|---:|\n| Studied online | 42 | 18 | 60 |\n| Studied in class | 56 | 24 | 80 |\n| Total | 98 | 42 | 140 |","difficulty":null,"difficultyBand":"medium","tier":null,"totalMarks":3,"sourceTitle":null,"calculatorUse":null,"isCalculation":false,"parts":[{"id":"eccf8337-03ae-409b-a801-347c4ce30905","label":null,"content":"Determine whether passing and study method are independent.","markscheme":"- $P(\\text{pass}\\cap\\text{online})=42/140=0.3$ M1\n- $P(\\text{pass})P(\\text{online})=(98/140)(60/140)=0.3$ M1\n- The probabilities are equal, so the events are independent A1","marks":3,"order":0,"markingRubric":null,"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"a_level_maths__ccea","summaries":[{"id":"e0ee0041-eba9-4711-a589-4b643be349f3","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"3e4b3412-9357-44fb-a7f0-0dd1b041f9d1","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"548b2e21-80f4-41df-a27e-781611dc3e2c","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"a56db217-c2ad-4e0c-bdbb-895515395538","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"fea00a84-116a-4352-8982-96617ed2ae3a","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"dc94f6e8-c98b-47aa-97bf-576fe36bb390","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"a60bbb4f-8fa4-4d9f-a8f1-f254adcd3417","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"f094c387-ff2b-43d9-8c55-a818499bb58f","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"2c4c5027-1916-41c4-b868-7127a15b4873","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"e58cf269-2e4b-4666-b503-1008b988a885","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"0f825110-b5d1-4081-9a67-ba2aae6d48aa","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"157d146d-64bd-4578-b16a-4aaba18e53af","difficultyBand":"hard","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"1e141ea8-4a38-44fa-b39f-700f0dde234c","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"340526b8-5e66-4b99-a900-d10cfad45991","difficultyBand":"hard","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"38944a11-484d-4978-8656-789fc8881e8c","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"459a69ca-160c-4c2f-b0f4-b0426e34f296","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"51326e4f-2b19-403b-a86b-a2e2b91579e1","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"5db91edf-8a94-4a91-9244-d4daa7a46fb6","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6c0ec4c3-6bc8-4f61-aacc-a7785668fe33","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"6f025f2e-c50d-4bf6-b77c-a1bde2e971a2","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"6f08c4a2-a3de-42d7-a0ce-f66cfbec0d00","difficultyBand":"hard","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"782c2c97-de93-4da6-84bf-09960ecc271d","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"7c92c5fa-9331-40da-863e-f2d49d629863","difficultyBand":"hard","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"82840219-b018-45e6-b9cd-8858d117e624","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"8607ef20-687f-4fec-81f6-74e6b0687b0a","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"8732a01f-5432-4aac-917d-7a3f4989b3ff","difficultyBand":"hard","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"8e070193-dd5b-456f-9bcc-1a8fabf34382","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"962ae054-c627-4242-8213-c72a3d781509","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"a2af0b6a-5458-47c7-8cfe-a4def00c8328","difficultyBand":"hard","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"aa01507f-f397-4a1a-9981-a4cd47179c9a","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"aae4c758-faa5-4852-9fd5-67cdfeeefde0","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"b17f4419-4071-48ea-8de9-c2b61650d867","difficultyBand":"hard","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"b1d2f540-302d-4877-a546-a8aa49bf2a76","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"b7899080-3906-4ced-ab46-e772c7a8b4ea","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"bbff1ee6-fa6f-4218-bff0-e42164b52d94","difficultyBand":"hard","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"eb5ad565-ee7c-4ac8-a798-711fc7065701","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true}],"title":"2.6 Probability","topicId":"712e3768-c7f1-4828-9533-c640dcaf6db9","topicSidebar":"$L3c","topicSlug":"probability","topicTitle":"2.6 Probability"}]}],"$L3d","$L3e"]}]

2.6 Probability

Question 18

2.6 Probability Questions

2.6 Probability

Question 18

2.6 Probability Questions