{
  "title": "Random Experiments - Grade 9 Probability",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is a random experiment in probability?", "options": {"A": "An experiment with fixed outcome", "B": "An experiment where outcome cannot be predicted", "C": "A scientific experiment", "D": "A mathematical proof"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Which of these is a random experiment?", "options": {"A": "Measuring length of a table", "B": "Rolling a die", "C": "Solving 2+2", "D": "Reading a book"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "In probability, what does 'trial' mean?", "options": {"A": "The result of experiment", "B": "Single performance of random experiment", "C": "The sample space", "D": "The probability value"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Which is NOT a random experiment?", "options": {"A": "Tossing a coin", "B": "Drawing a card from deck", "C": "Measuring your height", "D": "Spinning a wheel"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "What characteristic defines a random experiment?", "options": {"A": "Repeatable under same conditions", "B": "Has only one possible outcome", "C": "Always gives same result", "D": "Never been done before"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Flipping a coin is an example of:", "options": {"A": "Certain event", "B": "Random experiment", "C": "Impossible event", "D": "Deterministic process"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "In a random experiment, can we predict the exact outcome?", "options": {"A": "Always", "B": "Sometimes", "C": "Never", "D": "Only with practice"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Which property must a random experiment have?", "options": {"A": "More than one possible outcome", "B": "Only two outcomes", "C": "Outcome must be a number", "D": "Must use dice or coins"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Selecting a student randomly from class is:", "options": {"A": "Random experiment", "B": "Certain selection", "C": "Impossible task", "D": "Deterministic process"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "What makes an experiment 'random'?", "options": {"A": "Outcome is known beforehand", "B": "Outcome depends on chance", "C": "It involves randomness in name", "D": "It's done randomly"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Drawing a marble from a bag without looking is:", "options": {"A": "Random experiment", "B": "Certain event", "C": "Impossible event", "D": "Determined outcome"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Which of these is deterministic, not random?", "options": {"A": "Rolling a die", "B": "Sun rising tomorrow", "C": "Coin toss result", "D": "Lottery draw"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "How many possible outcomes in tossing two coins?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "A random experiment must be:", "options": {"A": "Repeatable", "B": "Unique", "C": "Done only once", "D": "Secret"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Spinning a roulette wheel is:", "options": {"A": "Random experiment", "B": "Certain outcome", "C": "Predetermined result", "D": "Not an experiment"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "What does 'equally likely' mean in random experiments?", "options": {"A": "All outcomes have same chance", "B": "Some outcomes more likely", "C": "Outcomes are numbers", "D": "Experiment is fair"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Choosing a random day of week is:", "options": {"A": "Random experiment", "B": "Certain selection", "C": "Predictable", "D": "Not probabilistic"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "In a fair die roll, each outcome is:", "options": {"A": "Equally likely", "B": "Different probabilities", "C": "Certain", "D": "Impossible"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "What's needed before performing probability calculations?", "options": {"A": "Define random experiment", "B": "Guess the answer", "C": "Know all outcomes", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 20, "difficulty": "easy", "question": "Random experiments help us study:", "options": {"A": "Certainty", "B": "Chance and uncertainty", "C": "Exact measurements", "D": "Mathematical proofs"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "Which characteristic is NOT required for random experiment?", "options": {"A": "More than one possible outcome", "B": "Outcome depends on chance", "C": "Can be repeated under same conditions", "D": "Must use physical objects"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "In probability theory, why are random experiments important?", "options": {"A": "They model real-world uncertainty", "B": "They give exact answers", "C": "They eliminate chance", "D": "They prove theorems"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Selecting a random number between 1-100 is random experiment because:", "options": {"A": "Outcome unpredictable but possible outcomes known", "B": "We can predict the number", "C": "Only one outcome possible", "D": "It's always 50"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Two characteristics of random experiments are:", "options": {"A": "Repeatability and uncertainty", "B": "Certainty and uniqueness", "C": "Predictability and stability", "D": "Singularity and determination"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Weather prediction is based on:", "options": {"A": "Deterministic experiment", "B": "Random experiment concepts", "C": "Exact calculations", "D": "Pure guesswork"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "What's the difference between trial and experiment?", "options": {"A": "Experiment is single performance, trial is overall concept", "B": "Trial is single performance, experiment is overall concept", "C": "They mean the same", "D": "Experiment is always bigger"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Why is 'measuring temperature at noon' not perfectly random?", "options": {"A": "It's somewhat predictable based on weather patterns", "B": "It has only one outcome", "C": "It cannot be repeated", "D": "It's completely deterministic"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "In a biased coin toss (60% heads), is it still a random experiment?", "options": {"A": "Yes, outcome still uncertain", "B": "No, because probabilities unequal", "C": "No, outcome predictable", "D": "Only if fair"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "What makes rolling two dice different from rolling one die twice?", "options": {"A": "Sample space size", "B": "Both are same random experiment", "C": "One is random, other not", "D": "Different probability concepts"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Choosing a card from well-shuffled deck ensures:", "options": {"A": "Each card equally likely", "B": "Certain card will be chosen", "C": "No uncertainty", "D": "Predictable outcome"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "A 'fair' random experiment means:", "options": {"A": "All outcomes equally likely", "B": "Experiment is just", "C": "Outcome is fair", "D": "Conducted properly"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Random sampling in surveys uses principles of:", "options": {"A": "Random experiments", "B": "Certain selection", "C": "Biased choosing", "D": "Predictive analysis"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "What condition violates 'random experiment' definition?", "options": {"A": "Only one possible outcome", "B": "Multiple outcomes", "C": "Outcome uncertain", "D": "Repeatable"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "In probability, why do we consider 'ideal' random experiments?", "options": {"A": "To simplify mathematical modeling", "B": "Real experiments are never random", "C": "To make calculations harder", "D": "Because they don't exist"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Selecting a random student for quiz is random experiment if:", "options": {"A": "Selection method ensures equal chance for all", "B": "Teacher chooses favorite", "C": "First student always selected", "D": "Selection is predetermined"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "What's the key difference between deterministic and random processes?", "options": {"A": "Predictability of outcome", "B": "Number of outcomes", "C": "Complexity", "D": "Mathematical representation"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "A loaded die (weighted) still represents:", "options": {"A": "Random experiment with unequal probabilities", "B": "Deterministic process", "C": "Not a valid experiment", "D": "Certain outcome experiment"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Why is 'sun rising tomorrow' not treated as random experiment?", "options": {"A": "Outcome is certain (practically)", "B": "Has multiple outcomes", "C": "Cannot be repeated", "D": "Involves chance"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "In random experiment, sample space must be:", "options": {"A": "Known before experiment", "B": "Determined after experiment", "C": "Always numerical", "D": "Small and finite"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "What ensures 'randomness' in card drawing?", "options": {"A": "Proper shuffling", "B": "Looking at cards", "C": "Choosing top card always", "D": "Knowing the deck order"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Multiple trials of same random experiment should be:", "options": {"A": "Independent", "B": "Dependent", "C": "Identical in outcome", "D": "Connected"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Which real-life situation best models random experiment?", "options": {"A": "Lottery draw", "B": "Sunset time", "C": "2+2 calculation", "D": "Your birthday"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "What does 'with replacement' mean in random experiments?", "options": {"A": "Item returned before next draw", "B": "Item kept out", "C": "Experiment repeated exactly", "D": "Different sample space"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "A perfectly shuffled deck represents:", "options": {"A": "Ideal random experiment setup", "B": "Biased selection", "C": "Deterministic arrangement", "D": "Predictable outcome"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Why are coins and dice commonly used in probability examples?", "options": {"A": "Simple, familiar, model fair random experiments", "B": "They are always available", "C": "They give complex outcomes", "D": "Historical reasons only"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "What does 'without replacement' change about random experiment?", "options": {"A": "Probabilities change each trial", "B": "Experiment becomes deterministic", "C": "Sample space disappears", "D": "Outcomes become certain"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "In random experiment, 'event' is:", "options": {"A": "Subset of sample space", "B": "The experiment itself", "C": "The outcome", "D": "The probability"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "What distinguishes 'fair' from 'unfair' random experiment?", "options": {"A": "Equality of outcome probabilities", "B": "Number of outcomes", "C": "Type of objects used", "D": "Who conducts it"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Selecting a random password from possibilities is:", "options": {"A": "Random experiment with huge sample space", "B": "Deterministic process", "C": "Certain selection", "D": "Not an experiment"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Why must sample space be well-defined in random experiments?", "options": {"A": "For meaningful probability calculations", "B": "To impress mathematicians", "C": "It's optional", "D": "Only for complex experiments"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "What's the role of 'chance' in random experiments?", "options": {"A": "Determines actual outcome", "B": "Makes outcome certain", "C": "Eliminates possibilities", "D": "Creates sample space"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "How does 'random number generator' relate to random experiments?", "options": {"A": "Simulates ideal random experiment", "B": "Eliminates randomness", "C": "Makes outcomes certain", "D": "Not related to probability"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "What ensures 'fairness' in die rolling?", "options": {"A": "Symmetrical die, random throwing", "B": "Choosing favorite number", "C": "Controlled throwing", "D": "Using loaded die"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "In probability, what does 'equiprobable' refer to?", "options": {"A": "All outcomes equally likely", "B": "Experiment is proper", "C": "Sample space is large", "D": "Events are similar"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Why is 'selecting prime minister' not good random experiment?", "options": {"A": "Outcome not purely chance-based", "B": "Too many outcomes", "C": "Sample space unknown", "D": "Not repeatable"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "What aspect makes an experiment truly 'random'?", "options": {"A": "Lack of predictable pattern in outcomes", "B": "Using random objects", "C": "Being done quickly", "D": "Having many trials"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "How does sample space size affect random experiment?", "options": {"A": "Affects probability calculations", "B": "Makes experiment deterministic", "C": "Eliminates randomness", "D": "No effect"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "What's required for 'repeated trials' to be valid?", "options": {"A": "Same conditions each time", "B": "Different conditions", "C": "Changing sample space", "D": "Different experimenter"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "In what way are all random experiments similar?", "options": {"A": "Outcome uncertainty", "B": "Use of physical objects", "C": "Having two outcomes", "D": "Being fair"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Why do we study random experiments mathematically?", "options": {"A": "To quantify uncertainty", "B": "To eliminate chance", "C": "To predict exact outcomes", "D": "To make things random"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "What does 'independent trials' mean in random experiments?", "options": {"A": "One trial doesn't affect another", "B": "Trials are identical", "C": "Trials are different experiments", "D": "Outcomes are same"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "How is 'random experiment' different from 'experiment' in science?", "options": {"A": "Focus on chance vs. controlled conditions", "B": "One is real, other theoretical", "C": "No difference", "D": "Different equipment used"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "What ensures drawing cards is random experiment?", "options": {"A": "Cannot see cards, well-shuffled", "B": "Choosing from top", "C": "Looking at cards first", "D": "Selecting favorite suit"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Why is 'guessing answer on MCQ' a random experiment if unprepared?", "options": {"A": "Outcome depends on chance", "B": "You always know answer", "C": "Only one option possible", "D": "Not an experiment"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "What makes rolling die 'fair' random experiment?", "options": {"A": "Symmetrical die, random roll", "B": "Choosing how it lands", "C": "Using special surface", "D": "Always getting 6"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "How does 'sample space' relate to random experiment?", "options": {"A": "It lists all possible outcomes", "B": "It predicts the outcome", "C": "It eliminates outcomes", "D": "It changes during experiment"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "In random experiment, can probability be 1 for some outcome?", "options": {"A": "Yes, for certain events", "B": "No, always less than 1", "C": "Only for impossible events", "D": "Never in random experiments"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "What distinguishes 'theoretical' from 'experimental' probability?", "options": {"A": "Calculation vs. actual trials", "B": "One is random, other not", "C": "Different sample spaces", "D": "No real difference"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Why must random experiment be 'repeatable'?", "options": {"A": "To verify probability predictions", "B": "To get same outcome", "C": "To make it deterministic", "D": "To change sample space"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "What does 'mutually exclusive' mean in random experiments?", "options": {"A": "Events cannot occur together", "B": "Events always occur together", "C": "Events have same probability", "D": "Events are independent"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "How does bias affect random experiment?", "options": {"A": "Changes probability distribution", "B": "Makes it deterministic", "C": "Eliminates sample space", "D": "No effect if small"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "What's the purpose of defining random experiment clearly?", "options": {"A": "Avoid ambiguity in probability calculations", "B": "Make it more random", "C": "Increase sample space", "D": "Reduce number of trials"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "In random experiment, what is 'elementary event'?", "options": {"A": "Single outcome", "B": "Set of outcomes", "C": "The experiment itself", "D": "Probability value"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Why are coin tosses considered 'ideal' random experiments?", "options": {"A": "Simple, two equally likely outcomes", "B": "Always gives heads", "C": "Outcome can be controlled", "D": "Sample space is infinite"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "What does 'exhaustive' mean for events in random experiment?", "options": {"A": "Cover all possible outcomes", "B": "Exclude some outcomes", "C": "Are independent", "D": "Have equal probability"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "How does 'with replacement' affect probability calculations?", "options": {"A": "Probabilities remain constant", "B": "Probabilities decrease", "C": "Probabilities increase", "D": "No effect"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "What ensures 'independence' in repeated trials?", "options": {"A": "Outcome of one doesn't affect next", "B": "Same outcome each time", "C": "Different sample spaces", "D": "Changing conditions"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Why is 'random experiment' foundational in probability?", "options": {"A": "Defines context for probability calculations", "B": "It's optional concept", "C": "Only for complex problems", "D": "Historical concept only"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "What does 'random' imply in practical experiments?", "options": {"A": "No pattern or predictability", "B": "Quick execution", "C": "Multiple experimenters", "D": "Use of special equipment"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "How do 'real-world' random experiments differ from 'ideal'?", "options": {"A": "May have slight biases", "B": "Have different mathematics", "C": "Not truly random", "D": "Cannot be analyzed"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "In quantum mechanics, particle position measurement is random experiment because:", "options": {"A": "Outcome fundamentally unpredictable", "B": "We don't have good instruments", "C": "Particles are too small", "D": "It's actually deterministic"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "What philosophical problem arises with 'true randomness'?", "options": {"A": "Whether it truly exists or is just unknown complexity", "B": "It's too simple", "C": "Cannot be mathematical", "D": "Nobody studies it"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "How does 'pseudorandom' in computers affect probability theory?", "options": {"A": "Good enough for most applications if properly seeded", "B": "Makes all calculations invalid", "C": "Eliminates need for probability", "D": "Creates true randomness"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "In Bayesian probability, how is random experiment conceptualized?", "options": {"A": "As subjective uncertainty even with fixed outcome", "B": "Only as frequency of outcomes", "C": "Not used at all", "D": "Same as classical view"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "What's the 'principle of indifference' in random experiments?", "options": {"A": "Assign equal probability when no reason to think otherwise", "B": "Ignore some outcomes", "C": "Be indifferent to results", "D": "Randomly choose probabilities"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "How do 'almost sure' events differ in infinite random experiments?", "options": {"A": "Probability 1 but may not occur in finite trials", "B": "Always occur", "C": "Never occur", "D": "Have probability 0"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "What's the 'measure theory' approach to random experiments?", "options": {"A": "Generalizes to continuous and complex sample spaces", "B": "Only for discrete cases", "C": "Simplifies to counting", "D": "Eliminates randomness"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "In stochastic processes, how are random experiments extended?", "options": {"A": "To sequences of experiments evolving over time", "B": "Made deterministic", "C": "Eliminated", "D": "Simplified to single trial"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "What's the 'frequentist' interpretation of random experiments?", "options": {"A": "Probability as long-term frequency", "B": "Probability as degree of belief", "C": "Probability as physical propensity", "D": "Probability as logical relation"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "How does 'conditional probability' modify view of random experiments?", "options": {"A": "Considers probability given partial information", "B": "Makes experiments deterministic", "C": "Eliminates sample space", "D": "Creates new experiments"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "What's 'Kolmogorov's axiomatic approach' to random experiments?", "options": {"A": "Mathematical foundation without philosophical interpretation", "B": "Only for fair experiments", "C": "Rejects real experiments", "D": "Based on physical symmetry"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "How do 'random variables' transform random experiments?", "options": {"A": "Assign numbers to outcomes for analysis", "B": "Make outcomes certain", "C": "Eliminate randomness", "D": "Create new sample spaces"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "What's the 'principle of sufficient reason' problem with random experiments?", "options": {"A": "If everything has cause, true randomness questionable", "B": "Experiments need sufficient trials", "C": "Sample space must be sufficient", "D": "Probability must be sufficient"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "In ergodic theory, how are random experiments characterized?", "options": {"A": "Time averages equal ensemble averages", "B": "Always produce same outcome", "C": "Never repeat patterns", "D": "Have infinite sample space"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "What's the 'de Finetti's theorem' significance for random experiments?", "options": {"A": "Exchangeable sequences represent conditionally independent trials", "B": "All experiments are independent", "C": "Randomness doesn't exist", "D": "Probability always subjective"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "How does 'quantum randomness' challenge classical random experiment concepts?", "options": {"A": "Suggests fundamental indeterminism", "B": "Proves all is deterministic", "C": "Eliminates probability", "D": "Makes experiments unnecessary"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "What's the 'Borel-Kolmogorov paradox' about random experiments?", "options": {"A": "Conditional probability on sets of measure zero", "B": "Experiments with no outcomes", "C": "Infinite sample spaces", "D": "Biased experiments"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "In algorithmic information theory, how is randomness defined?", "options": {"A": "As incompressibility of outcome sequences", "B": "As unpredictability", "C": "As equal probabilities", "D": "As physical symmetry"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "What's the 'reference class problem' for random experiments?", "options": {"A": "Which sample space to use for single case", "B": "Too many outcomes", "C": "Experiments too complex", "D": "Probability always 0 or 1"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "How do 'martingales' extend concept of random experiments?", "options": {"A": "Model fair games with evolving information", "B": "Make all games unfair", "C": "Eliminate chance", "D": "Only for independent trials"}, "correct_answer": "A"}
  ]
}