[
  {
    "id": "book-oi-20260912-001",
    "section": "quant",
    "topic": "Independent events",
    "prompt": "A fair coin is tossed independently. The last eight tosses were all heads. What is the probability that the next toss is heads?",
    "options": [
      "1/256",
      "1/9",
      "1/4",
      "1/2",
      "8/9"
    ],
    "answer": 3,
    "explanation": "Independence means earlier outcomes do not change the next toss. A fair coin still has probability 1/2 of heads.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: True or false, part (a)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/defining_probability.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "True or false, part (a)",
    "sourceFile": "defining_probability.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-002",
    "section": "quant",
    "topic": "Independent events",
    "prompt": "A roulette wheel has 38 equally likely slots: 18 red, 18 black and 2 green. Assume spins are independent. After three consecutive red outcomes, what is the probability of red on the next spin?",
    "options": [
      "3/38",
      "9/19",
      "1/2",
      "18/35",
      "3/4"
    ],
    "answer": 1,
    "explanation": "There are 18 red slots among 38 equally likely slots, so the probability is 18/38 = 9/19. Earlier spins do not change it.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Roulette wheel, part (a)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/defining_probability.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Roulette wheel, part (a)",
    "sourceFile": "defining_probability.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-003",
    "section": "quant",
    "topic": "Probability",
    "prompt": "A fair coin is tossed independently 10 times. What is the probability that all 10 outcomes are tails?",
    "options": [
      "1/20",
      "1/100",
      "1/512",
      "1/1024",
      "1/2048"
    ],
    "answer": 3,
    "explanation": "Multiply ten factors of 1/2: (1/2)^10 = 1/1024.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Coin flips, part (a)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/defining_probability.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Coin flips, part (a)",
    "sourceFile": "defining_probability.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-004",
    "section": "quant",
    "topic": "Complementary probability",
    "prompt": "A fair coin is tossed independently 10 times. What is the probability of observing at least one tail?",
    "options": [
      "1/1024",
      "1/2",
      "9/10",
      "511/512",
      "1023/1024"
    ],
    "answer": 4,
    "explanation": "The complement is all heads, with probability 1/1024. Subtracting this from 1 gives 1023/1024.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Coin flips, part (c)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/defining_probability.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Coin flips, part (c)",
    "sourceFile": "defining_probability.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-005",
    "section": "quant",
    "topic": "Probability",
    "prompt": "Two fair six-sided dice are rolled independently. What is the probability that the sum is 5?",
    "options": [
      "1/36",
      "1/12",
      "1/9",
      "5/36",
      "1/6"
    ],
    "answer": 2,
    "explanation": "The four favorable ordered pairs are (1,4), (2,3), (3,2), and (4,1). There are 36 equally likely pairs, so 4/36 = 1/9.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Dice rolls, part (b)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/defining_probability.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Dice rolls, part (b)",
    "sourceFile": "defining_probability.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-006",
    "section": "quant",
    "topic": "Probability",
    "prompt": "An exam contains 5 multiple-choice questions, each with 4 options and exactly one correct answer. A student guesses uniformly and independently on every question. What is the probability that the first correct answer is on question 5?",
    "options": [
      "1/1024",
      "81/1024",
      "243/1024",
      "1/4",
      "5/16"
    ],
    "answer": 1,
    "explanation": "The student must get four questions wrong and the fifth right: (3/4)^4 × (1/4) = 81/1024.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Guessing on an exam, part (a)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/defining_probability.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Guessing on an exam, part (a)",
    "sourceFile": "defining_probability.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-007",
    "section": "quant",
    "topic": "Complementary probability",
    "prompt": "An exam has 5 questions, each with 4 options and exactly one correct answer. A student guesses uniformly and independently. What is the probability of at least one correct answer?",
    "options": [
      "1/1024",
      "5/1024",
      "243/1024",
      "781/1024",
      "1023/1024"
    ],
    "answer": 3,
    "explanation": "All five answers are wrong with probability (3/4)^5 = 243/1024. Its complement is 781/1024.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Guessing on an exam, part (c)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/defining_probability.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Guessing on an exam, part (c)",
    "sourceFile": "defining_probability.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-008",
    "section": "quant",
    "topic": "Probability distributions",
    "prompt": "The five entries in each option are proposed probabilities of grades A, B, C, D and F, respectively. Which option is a valid probability distribution?",
    "options": [
      "(0.3, 0.3, 0.3, 0.2, 0.1)",
      "(0.3, 0.3, 0.3, 0, 0)",
      "(0.3, 0.5, 0.2, 0.1, −0.1)",
      "(0.2, 0.4, 0.2, 0.1, 0.1)",
      "(0, −0.1, 1.1, 0, 0)"
    ],
    "answer": 3,
    "explanation": "Every probability must lie between 0 and 1, and their sum must be 1. Only the fourth option satisfies both conditions. The first sums to 1.2; the second to 0.9; the third and fifth contain negative entries.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Grade distributions, selected rows",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/review_exercises.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Grade distributions, selected rows",
    "sourceFile": "review_exercises.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-009",
    "section": "quant",
    "topic": "Expected value",
    "prompt": "A student buys one coffee and one muffin each morning. The mean coffee price is $1.40, and the mean muffin price is $2.50. What is the expected daily total?",
    "options": [
      "$1.95",
      "$2.50",
      "$3.50",
      "$3.90",
      "$4.20"
    ],
    "answer": 3,
    "explanation": "Expected values add: E(coffee + muffin) = 1.40 + 2.50 = $3.90. Independence is not needed to add means.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Cost of breakfast, part (a), mean only",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/review_exercises.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Cost of breakfast, part (a), mean only",
    "sourceFile": "review_exercises.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-010",
    "section": "quant",
    "topic": "Expected value",
    "prompt": "A student buys one coffee and one muffin on each of 7 days. On every day, the expected coffee price is $1.40 and the expected muffin price is $2.50. What is the expected total for the week?",
    "options": [
      "$19.60",
      "$24.50",
      "$26.30",
      "$27.30",
      "$28.00"
    ],
    "answer": 3,
    "explanation": "The expected daily cost is $3.90. Over seven days the expected sum is 7 × 3.90 = $27.30.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Cost of breakfast, part (b), mean only",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/review_exercises.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Cost of breakfast, part (b), mean only",
    "sourceFile": "review_exercises.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-011",
    "section": "quant",
    "topic": "Expected value",
    "prompt": "The amount of ice cream in a box has mean 48 fluid ounces. One scoop has mean 2 fluid ounces. What is the expected amount left after removing one scoop?",
    "options": [
      "24 fluid ounces",
      "44 fluid ounces",
      "46 fluid ounces",
      "48 fluid ounces",
      "50 fluid ounces"
    ],
    "answer": 2,
    "explanation": "Linearity gives E(box − scoop) = 48 − 2 = 46 fluid ounces.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Scooping ice cream, part (b), expectation only",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/review_exercises.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Scooping ice cream, part (b), expectation only",
    "sourceFile": "review_exercises.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-012",
    "section": "quant",
    "topic": "Expected value",
    "prompt": "An entire box of ice cream and three scoops from another box are served. A box contains an expected 48 fluid ounces, and each scoop has expected volume 2 fluid ounces. What is the expected total served?",
    "options": [
      "50 fluid ounces",
      "52 fluid ounces",
      "54 fluid ounces",
      "96 fluid ounces",
      "144 fluid ounces"
    ],
    "answer": 2,
    "explanation": "Add the expected box volume and the three expected scoop volumes: 48 + 3 × 2 = 54 fluid ounces.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Scooping ice cream, part (a), expectation only",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/review_exercises.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Scooping ice cream, part (a), expectation only",
    "sourceFile": "review_exercises.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-013",
    "section": "quant",
    "topic": "Expected value",
    "prompt": "For this exercise, suppose 13% of students at a university smoke. In a simple random sample of 100 students from that university, what is the expected number who smoke?",
    "options": [
      "0.13",
      "1.3",
      "10",
      "13",
      "87"
    ],
    "answer": 3,
    "explanation": "Each sampled student has probability 0.13 of being a smoker. Summing 100 indicator expectations gives 100 × 0.13 = 13. This is an exercise assumption, not a claim about current smoking rates.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: College smokers, part (a)",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/random_variables.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "College smokers, part (a)",
    "sourceFile": "random_variables.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-014",
    "section": "quant",
    "topic": "Weighted average",
    "prompt": "In a hypothetical model, a portfolio returns +18% in a boom, +9% in normal conditions, and −12% in a recession. If the three scenarios are equally likely, what is its expected percentage return?",
    "options": [
      "−5%",
      "3%",
      "5%",
      "9%",
      "13%"
    ],
    "answer": 2,
    "explanation": "Average the three equally likely returns, retaining the negative sign: (18 + 9 − 12)/3 = 5%. This is a mathematical model, not an investment forecast.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Portfolio return",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/random_variables.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Portfolio return",
    "sourceFile": "random_variables.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-015",
    "section": "quant",
    "topic": "Expected value",
    "prompt": "An airline charges $25 for the first checked bag and an additional $35 for the second. Suppose 54% of passengers check no bags, 34% check one and 12% check two, with nobody checking more than two. What is the expected baggage-fee revenue per passenger?",
    "options": [
      "$8.50",
      "$12.70",
      "$15.70",
      "$27.60",
      "$60.00"
    ],
    "answer": 2,
    "explanation": "The fees for zero, one and two bags are $0, $25 and $60. The weighted mean is 0(0.54) + 25(0.34) + 60(0.12) = $15.70.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Baggage fees, part (a), mean only",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/random_variables.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Baggage fees, part (a), mean only",
    "sourceFile": "random_variables.tex",
    "sourceCheckedOn": "2026-09-12"
  },
  {
    "id": "book-oi-20260912-016",
    "section": "quant",
    "topic": "Expected value",
    "prompt": "One card is drawn uniformly from a standard 52-card deck without jokers. A red card pays $0, a spade pays $5, and a club pays $10, with an extra $20 for the ace of clubs. What is the expected payout, rounded to the nearest cent?",
    "options": [
      "$3.75",
      "$4.13",
      "$4.52",
      "$5.00",
      "$10.00"
    ],
    "answer": 1,
    "explanation": "There are 26 red cards, 13 spades, 12 non-ace clubs and one ace of clubs. The expected payout is (26×0 + 13×5 + 12×10 + 1×30)/52 = 215/52 ≈ $4.13. No entry fee is specified.",
    "source": "Adapted from OpenIntro Statistics — David M. Diez, Mine Çetinkaya-Rundel and Christopher D. Barr; exercise: Ace of clubs wins, part (a), expectation only",
    "sourceUrl": "https://github.com/OpenIntroStat/openintro-statistics/blob/master/ch_probability/TeX/random_variables.tex",
    "license": "CC BY-SA 3.0: original exercise and this adaptation. https://creativecommons.org/licenses/by-sa/3.0/ Changes: wording condensed, selected subparts converted to single-answer multiple choice, assumptions clarified; options and explanations added by GRE Studio. No endorsement by the original authors.",
    "licenseUrl": "https://creativecommons.org/licenses/by-sa/3.0/",
    "sourceExercise": "Ace of clubs wins, part (a), expectation only",
    "sourceFile": "random_variables.tex",
    "sourceCheckedOn": "2026-09-12"
  }
]