{
  "title": "Theoretical Probability - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A fair die 🎲 is rolled. What is the theoretical probability of getting a 4? 🎯", "options": {"A": "1/2", "B": "1/3", "C": "1/6", "D": "1/4"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "A coin 🪙 is tossed. What is P(heads) theoretically? 💡", "options": {"A": "0", "B": "0.25", "C": "0.5", "D": "1"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "A bag has 5 red 🔴 and 3 blue 🔵 balls. One ball drawn randomly. What's P(blue)?", "options": {"A": "3/8", "B": "5/8", "C": "1/2", "D": "2/5"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "A card 🃏 drawn from a well-shuffled deck. What's P(ace)? 👑", "options": {"A": "1/52", "B": "1/13", "C": "1/4", "D": "4/13"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "What is the theoretical probability of getting an odd number on a die roll? 🎲", "options": {"A": "1/6", "B": "1/3", "C": "1/2", "D": "2/3"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "A month 📅 picked randomly. What's P(month starting with J)?", "options": {"A": "1/12", "B": "1/6", "C": "1/4", "D": "1/3"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "A letter chosen from 'SCHOOL'. What's P(letter O)? 🔤", "options": {"A": "1/3", "B": "1/6", "C": "1/2", "D": "2/3"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Two coins 🪙🪙 tossed. What's P(two tails)?", "options": {"A": "1/4", "B": "1/2", "C": "3/4", "D": "1"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "A number from 1 to 10 chosen. What's P(prime)? 🔢", "options": {"A": "2/5", "B": "3/5", "C": "1/2", "D": "7/10"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "A spinner ⭕ has 8 equal sectors numbered 1-8. What's P(landing on 5)?", "options": {"A": "1/4", "B": "1/8", "C": "1/2", "D": "3/8"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "A bag: 4 white ⚪, 6 black ⚫ balls. One ball drawn. What's P(white)?", "options": {"A": "2/5", "B": "3/5", "C": "1/2", "D": "4/5"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "A day chosen from a week. What's P(not Sunday)? 📅", "options": {"A": "1/7", "B": "2/7", "C": "6/7", "D": "5/7"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "A card 🃏 drawn from deck. What's P(diamond)? ♦️", "options": {"A": "1/52", "B": "1/13", "C": "1/4", "D": "13/52"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "A die 🎲 rolled. What's P(number > 4)?", "options": {"A": "1/6", "B": "1/3", "C": "1/2", "D": "2/3"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "A letter from 'PROBABILITY' chosen. What's P(B)? 🔠", "options": {"A": "1/11", "B": "2/11", "C": "3/11", "D": "4/11"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "A bag with 3 red, 2 green 🟢, 5 yellow 💛 marbles. One drawn. What's P(not yellow)?", "options": {"A": "1/2", "B": "1/5", "C": "1/3", "D": "2/5"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "A number from 1-20 chosen. What's P(multiple of 5)? ✨", "options": {"A": "1/10", "B": "1/5", "C": "3/10", "D": "1/4"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "A true/false question answered randomly. What's P(correct)? ✔️", "options": {"A": "0.25", "B": "0.5", "C": "0.75", "D": "1"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "A baby 👶 born. What's P(boy)? 👦", "options": {"A": "0", "B": "0.25", "C": "0.5", "D": "1"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "A card 🃏 drawn from deck. What's P(black card)? ♠️♣️", "options": {"A": "1/4", "B": "1/2", "C": "3/4", "D": "1"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "medium", "question": "Two dice 🎲🎲 rolled. What's theoretical P(sum = 9)? 🧮", "options": {"A": "1/9", "B": "1/6", "C": "5/36", "D": "1/12"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "A card 🃏 drawn from deck. What's P(red queen)? ♥️♦️👑", "options": {"A": "1/26", "B": "1/13", "C": "1/52", "D": "2/13"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "A bag: 6 red, 4 blue marbles. Two marbles drawn without replacement. What's P(both red)? 🔴🔴", "options": {"A": "1/3", "B": "2/9", "C": "3/10", "D": "5/18"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Three coins 🪙🪙🪙 tossed. What's P(exactly two tails)?", "options": {"A": "1/8", "B": "3/8", "C": "1/2", "D": "5/8"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "From numbers 1-30, one chosen. What's P(divisible by 3 or 5)? 🔢", "options": {"A": "1/2", "B": "7/15", "C": "8/15", "D": "3/5"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "A committee of 2 from 4 boys 👦 and 3 girls 👧. What's P(both girls)?", "options": {"A": "1/7", "B": "2/7", "C": "3/7", "D": "4/7"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "A letter from 'MATHEMATICS' chosen. What's P(vowel)? 🔤", "options": {"A": "4/11", "B": "5/11", "C": "6/11", "D": "7/11"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Two dice 🎲🎲 rolled. What's P(doublet)?", "options": {"A": "1/12", "B": "1/6", "C": "1/4", "D": "1/3"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "A bag with balls numbered 1-15. One drawn. What's P(number divisible by 2 and 3)? ✨", "options": {"A": "1/15", "B": "2/15", "C": "1/5", "D": "4/15"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "A card 🃏 drawn from deck. What's P(king or spade)? 👑♠️", "options": {"A": "4/13", "B": "17/52", "C": "1/4", "D": "5/13"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Three coins 🪙🪙🪙 tossed. What's P(at most one head)?", "options": {"A": "1/2", "B": "3/8", "C": "1/4", "D": "1/8"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "A number from 1-50 chosen. What's P(perfect cube)? 🔲", "options": {"A": "1/25", "B": "2/25", "C": "3/50", "D": "1/10"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "A bag: 5 black ⚫, 3 white ⚪ balls. Two balls drawn. What's P(same color)?", "options": {"A": "13/28", "B": "15/28", "C": "1/2", "D": "3/7"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "A die 🎲 rolled twice. What's P(first roll even, second roll odd)? 📊", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/6"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "From word 'CALCULUS', a letter chosen. What's P(consonant)? 🔠", "options": {"A": "3/8", "B": "5/8", "C": "1/2", "D": "3/4"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Two cards 🃏🃏 drawn from deck without replacement. What's P(both face cards)? 👑👑", "options": {"A": "11/221", "B": "1/13", "C": "3/13", "D": "9/169"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "A die 🎲 rolled. Events: A={even}, B={<4}. What's P(A∩B)? 📈", "options": {"A": "1/6", "B": "1/3", "C": "1/2", "D": "2/3"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "A bag: 4 red, 5 blue, x green marbles. P(red)=1/5. Find x. 🟢", "options": {"A": "9", "B": "10", "C": "11", "D": "12"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "A family has 3 children 👦👧. What's P(at least one girl)?", "options": {"A": "1/8", "B": "3/8", "C": "1/2", "D": "7/8"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "A number from 1-100 chosen. What's P(divisible by 7)? 🔢", "options": {"A": "7/50", "B": "3/20", "C": "1/7", "D": "2/25"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "Three dice 🎲🎲🎲 rolled. What's theoretical P(sum = 10)? 🧮", "options": {"A": "1/8", "B": "1/12", "C": "1/18", "D": "1/24"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "A bag: 3 red, 4 blue, 5 green marbles. Three drawn without replacement. What's P(all different)? 🌈", "options": {"A": "3/11", "B": "4/11", "C": "5/11", "D": "6/11"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "A card 🃏 drawn from deck. What's P(neither heart ❤️ nor queen 👑)?", "options": {"A": "9/13", "B": "35/52", "C": "19/26", "D": "11/13"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "Two dice 🎲🎲 rolled. What's P(sum is prime and <7)? 🔢", "options": {"A": "5/36", "B": "1/6", "C": "7/36", "D": "2/9"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "A speaks truth 4/5 times, B speaks truth 3/4 times. They independently report an event. What's P(both lie)? 🤥", "options": {"A": "1/20", "B": "1/10", "C": "3/20", "D": "1/5"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "hard", "question": "A bag has 12 balls: some white ⚪, some black ⚫. P(two white)=5/33. How many white balls? 🤔", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "Three letters of 'BANANA' chosen. What's P(all A)? 🔤", "options": {"A": "1/20", "B": "1/10", "C": "1/5", "D": "3/20"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "A die 🎲 rolled 3 times. What's P(sum is odd)? ✨", "options": {"A": "1/2", "B": "3/8", "C": "5/8", "D": "7/8"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "From numbers 1-60, one chosen. What's P(divisible by 4 or 6)? 🔢", "options": {"A": "1/3", "B": "11/30", "C": "2/5", "D": "7/15"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "A bag: 4 red, 6 blue, 8 green marbles. Two drawn. What's P(no green)? 🟢❌", "options": {"A": "5/51", "B": "10/51", "C": "15/51", "D": "20/51"}, "correct_answer": "A"},
       {
      "id": 51,
      "difficulty": "hard",
      "question": "Two cards 🃏🃏 drawn from a deck. What's P(one heart ❤️ and one diamond ♦️)?",
      "options": {
        "A": "13/102",
        "B": "26/663",
        "C": "1/17",
        "D": "13/221"
      },
      "correct_answer": "D"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "A number from 1–200 chosen randomly. What's P(perfect square)? 🔢",
      "options": {
        "A": "1/20",
        "B": "1/14",
        "C": "1/10",
        "D": "7/100"
      },
      "correct_answer": "B"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Two dice 🎲🎲 rolled. What's P(product > 20)?",
      "options": {
        "A": "5/18",
        "B": "7/36",
        "C": "11/36",
        "D": "1/3"
      },
      "correct_answer": "C"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "A box contains 7 red, 5 blue, 3 green balls. Two drawn. What's P(exactly one blue)? 🔵",
      "options": {
        "A": "15/91",
        "B": "30/91",
        "C": "35/91",
        "D": "40/91"
      },
      "correct_answer": "B"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "A drawer has 4 socks each of 5 colours. Randomly pick 2 socks. What's P(both same colour)? 🧦",
      "options": {
        "A": "1/20",
        "B": "1/5",
        "C": "4/25",
        "D": "1/10"
      },
      "correct_answer": "B"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "Three dice 🎲🎲🎲 rolled. What's P(all 3 numbers distinct)?",
      "options": {
        "A": "5/9",
        "B": "2/3",
        "C": "25/36",
        "D": "5/6"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "A bag has 6 red, 4 blue, 5 green balls. Three drawn. What's P(at least one green)? 🌿",
      "options": {
        "A": "1/3",
        "B": "2/3",
        "C": "5/9",
        "D": "7/9"
      },
      "correct_answer": "D"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "A coin tossed 4 times. What's P(exactly 2 heads)? 🪙",
      "options": {
        "A": "1/4",
        "B": "3/8",
        "C": "6/16",
        "D": "3/16"
      },
      "correct_answer": "C"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "A number from 1–100 chosen. What's P(number is prime)? 🔢",
      "options": {
        "A": "10/50",
        "B": "25/100",
        "C": "1/4",
        "D": "21/100"
      },
      "correct_answer": "D"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "Two cards drawn from a deck. What's P(both are black face cards)? ♠️♣️👑",
      "options": {
        "A": "1/221",
        "B": "2/663",
        "C": "1/442",
        "D": "1/110"
      },
      "correct_answer": "A"
    }
  ]
}