{
  "title": "Event & Intro to Probability - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is probability of getting head when tossing a coin?", "options": {"A": "1/2", "B": "1", "C": "0", "D": "1/4"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "What is probability of getting tail when tossing a coin?", "options": {"A": "1/2", "B": "1", "C": "0", "D": "1/4"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Probability of impossible event?", "options": {"A": "0", "B": "1", "C": "1/2", "D": "1/4"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Probability of certain event?", "options": {"A": "1", "B": "0", "C": "1/2", "D": "1/4"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "What is probability of getting 3 when rolling a die?", "options": {"A": "1/6", "B": "1/3", "C": "1/2", "D": "1"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "What is probability of getting even number on die?", "options": {"A": "1/2", "B": "1/3", "C": "1/6", "D": "2/3"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "What is probability of getting odd number on die?", "options": {"A": "1/2", "B": "1/3", "C": "1/6", "D": "2/3"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "What is probability of getting number > 4 on die?", "options": {"A": "1/3", "B": "1/2", "C": "1/6", "D": "2/3"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "What is probability of getting number < 7 on die?", "options": {"A": "1", "B": "0", "C": "1/2", "D": "1/6"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "What is probability of getting 8 on die?", "options": {"A": "0", "B": "1", "C": "1/6", "D": "1/2"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "A bag has 3 red, 2 blue balls. Probability of drawing red?", "options": {"A": "3/5", "B": "2/5", "C": "1/5", "D": "4/5"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "A bag has 4 white, 1 black balls. Probability of drawing white?", "options": {"A": "4/5", "B": "1/5", "C": "3/5", "D": "2/5"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Deck of cards has 52 cards. Probability of drawing ace?", "options": {"A": "1/13", "B": "1/4", "C": "1/52", "D": "4/52"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Deck of cards: Probability of drawing heart?", "options": {"A": "1/4", "B": "1/13", "C": "1/52", "D": "13/52"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Deck of cards: Probability of drawing king?", "options": {"A": "1/13", "B": "1/4", "C": "1/52", "D": "4/52"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Probability range is between?", "options": {"A": "0 to 1", "B": "-1 to 1", "C": "0 to 10", "D": "0 to 100"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "If event A is certain, P(A) = ?", "options": {"A": "1", "B": "0", "C": "0.5", "D": "0.75"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "If event B is impossible, P(B) = ?", "options": {"A": "0", "B": "1", "C": "0.5", "D": "0.25"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Tossing 2 coins, probability of 2 heads?", "options": {"A": "1/4", "B": "1/2", "C": "3/4", "D": "1"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Tossing 2 coins, probability of at least 1 head?", "options": {"A": "3/4", "B": "1/4", "C": "1/2", "D": "1"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Probability of getting prime number on die?", "options": {"A": "1/2", "B": "1/3", "C": "2/3", "D": "1/6"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Probability of getting composite number on die?", "options": {"A": "1/3", "B": "1/2", "C": "2/3", "D": "1/6"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Bag has 5 red, 7 blue balls. Probability of red?", "options": {"A": "5/12", "B": "7/12", "C": "5/7", "D": "7/5"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Bag has 3 green, 4 yellow, 5 pink balls. Probability of green?", "options": {"A": "1/4", "B": "1/3", "C": "5/12", "D": "1/12"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Two dice rolled. Probability sum = 7?", "options": {"A": "1/6", "B": "1/12", "C": "1/36", "D": "5/36"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Two dice rolled. Probability sum = 8?", "options": {"A": "5/36", "B": "1/9", "C": "1/6", "D": "1/12"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Two dice rolled. Probability sum = 12?", "options": {"A": "1/36", "B": "1/18", "C": "1/12", "D": "1/6"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Two dice rolled. Probability sum = 13?", "options": {"A": "0", "B": "1/36", "C": "1/12", "D": "1/6"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Two dice rolled. Probability both show same number?", "options": {"A": "1/6", "B": "1/36", "C": "1/12", "D": "5/36"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Two dice rolled. Probability different numbers?", "options": {"A": "5/6", "B": "1/6", "C": "1/2", "D": "2/3"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Deck of cards: Probability of face card?", "options": {"A": "3/13", "B": "1/13", "C": "1/4", "D": "4/13"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Deck of cards: Probability of black king?", "options": {"A": "1/26", "B": "1/13", "C": "1/52", "D": "2/52"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Deck of cards: Probability of diamond or heart?", "options": {"A": "1/2", "B": "1/4", "C": "3/4", "D": "2/3"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Deck of cards: Probability of ace or king?", "options": {"A": "2/13", "B": "1/13", "C": "4/13", "D": "8/52"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Tossing 3 coins, probability all heads?", "options": {"A": "1/8", "B": "1/4", "C": "3/8", "D": "1/2"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Tossing 3 coins, probability at least 1 head?", "options": {"A": "7/8", "B": "1/8", "C": "3/8", "D": "1/2"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Tossing 3 coins, probability exactly 2 heads?", "options": {"A": "3/8", "B": "1/8", "C": "1/4", "D": "1/2"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Number 1 to 10 written on cards. Probability of prime?", "options": {"A": "2/5", "B": "1/2", "C": "3/5", "D": "3/10"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Number 1 to 20. Probability multiple of 3?", "options": {"A": "3/10", "B": "1/3", "C": "7/20", "D": "1/4"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Number 1 to 20. Probability multiple of 4?", "options": {"A": "1/4", "B": "1/5", "C": "3/10", "D": "1/3"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "If P(E) = 0.7, what is P(not E)?", "options": {"A": "0.3", "B": "0.7", "C": "1.7", "D": "0.4"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If P(A) = 0.4, P(B) = 0.3, A and B mutually exclusive, P(A or B)?", "options": {"A": "0.7", "B": "0.12", "C": "0.1", "D": "0.58"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "If P(E) = 2/3, what is P(not E)?", "options": {"A": "1/3", "B": "2/3", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Sum of probabilities of all elementary events?", "options": {"A": "1", "B": "0", "C": "0.5", "D": "2"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Probability cannot be?", "options": {"A": "1.2", "B": "0.5", "C": "0", "D": "1"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "If P(E) = 0.05, what is P(not E)?", "options": {"A": "0.95", "B": "0.05", "C": "0.5", "D": "1.05"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "A and B mutually exclusive, P(A and B) = ?", "options": {"A": "0", "B": "1", "C": "P(A)×P(B)", "D": "P(A)+P(B)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "If P(A)=0.3, P(B)=0.4, P(A and B)=0.1, P(A or B)=?", "options": {"A": "0.6", "B": "0.7", "C": "0.12", "D": "0.58"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Probability of drawing vowel from alphabet?", "options": {"A": "5/26", "B": "1/5", "C": "21/26", "D": "1/26"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Probability of drawing consonant from alphabet?", "options": {"A": "21/26", "B": "5/26", "C": "1/26", "D": "20/26"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "Two dice rolled. Probability sum is prime?", "options": {"A": "15/36", "B": "1/2", "C": "5/12", "D": "7/12"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Two dice rolled. Probability sum is even?", "options": {"A": "1/2", "B": "1/3", "C": "2/3", "D": "5/12"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Two dice rolled. Probability sum divisible by 3?", "options": {"A": "1/3", "B": "1/2", "C": "5/12", "D": "7/12"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Two dice rolled. Probability product is 12?", "options": {"A": "1/9", "B": "1/12", "C": "1/18", "D": "1/36"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Three coins tossed. Probability at most 2 heads?", "options": {"A": "7/8", "B": "1/8", "C": "3/8", "D": "5/8"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Three coins tossed. Probability at least 2 tails?", "options": {"A": "1/2", "B": "3/8", "C": "1/8", "D": "5/8"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Bag has 5 red, 4 blue, 3 green. Probability not red?", "options": {"A": "7/12", "B": "5/12", "C": "1/3", "D": "2/3"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Bag has 6 white, 4 black. Two balls drawn. Probability both white?", "options": {"A": "1/3", "B": "2/15", "C": "3/10", "D": "1/2"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "Bag: 5 red, 7 blue. Two balls drawn. Probability different colors?", "options": {"A": "35/66", "B": "5/33", "C": "7/33", "D": "10/33"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Cards: Probability of spade or ace?", "options": {"A": "4/13", "B": "1/13", "C": "1/4", "D": "17/52"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "hard", "question": "Cards: Probability of red or king?", "options": {"A": "7/13", "B": "1/2", "C": "15/26", "D": "8/13"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "hard", "question": "Cards: Probability of face card or heart?", "options": {"A": "11/26", "B": "1/2", "C": "3/13", "D": "4/13"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "hard", "question": "If P(A)=0.6, P(B)=0.5, P(A∩B)=0.3, find P(A∪B)", "options": {"A": "0.8", "B": "0.9", "C": "0.7", "D": "1.1"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "hard", "question": "If P(A)=0.4, P(B)=0.3, P(A∪B)=0.6, find P(A∩B)", "options": {"A": "0.1", "B": "0.12", "C": "0.7", "D": "0.2"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "hard", "question": "If P(A)=2/5, P(B)=1/3, P(A∩B)=1/15, find P(A∪B)", "options": {"A": "2/3", "B": "3/5", "C": "8/15", "D": "11/15"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "hard", "question": "If P(A)=0.7, P(B)=0.4, P(A∩B)=0.2, find P(only A)", "options": {"A": "0.5", "B": "0.2", "C": "0.3", "D": "0.7"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "hard", "question": "Events A,B independent. P(A)=0.3, P(B)=0.4, P(A∩B)=?", "options": {"A": "0.12", "B": "0.7", "C": "0.1", "D": "0.58"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "hard", "question": "Events A,B independent. P(A)=1/2, P(B)=1/3, P(A∪B)=?", "options": {"A": "2/3", "B": "1/6", "C": "5/6", "D": "1/3"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "hard", "question": "If P(A)=0.4, P(B)=0.5, P(A|B)=0.3, find P(A∩B)", "options": {"A": "0.15", "B": "0.2", "C": "0.12", "D": "0.18"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "hard", "question": "Probability of 53 Sundays in non-leap year?", "options": {"A": "1/7", "B": "2/7", "C": "52/365", "D": "53/365"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "hard", "question": "Probability of 53 Mondays in leap year?", "options": {"A": "2/7", "B": "1/7", "C": "52/366", "D": "53/366"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "hard", "question": "A speaks truth 3/4 times, B 4/5 times. Both say same fact, probability it's true?", "options": {"A": "12/13", "B": "1/2", "C": "3/5", "D": "4/5"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "hard", "question": "Bag has 3 red, 5 black. Two balls drawn without replacement. Probability first red, second black?", "options": {"A": "15/56", "B": "3/28", "C": "5/28", "D": "15/28"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "hard", "question": "Bag: 4 white, 3 red. Two drawn with replacement. Probability both white?", "options": {"A": "16/49", "B": "4/7", "C": "2/7", "D": "12/49"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "hard", "question": "Two dice rolled. Probability sum ≥ 10?", "options": {"A": "1/6", "B": "1/12", "C": "5/36", "D": "1/9"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "hard", "question": "Two dice rolled. Probability sum ≤ 5?", "options": {"A": "5/18", "B": "1/6", "C": "5/36", "D": "1/3"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "hard", "question": "Three dice rolled. Probability sum = 10?", "options": {"A": "1/8", "B": "1/12", "C": "1/36", "D": "1/216"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "hard", "question": "Four coins tossed. Probability exactly 3 heads?", "options": {"A": "1/4", "B": "3/8", "C": "1/2", "D": "1/8"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "hard", "question": "Five coins tossed. Probability at least 4 heads?", "options": {"A": "3/16", "B": "1/4", "C": "5/16", "D": "1/2"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "hard", "question": "Number 1-100. Probability divisible by 6 or 8?", "options": {"A": "1/4", "B": "3/10", "C": "1/5", "D": "11/50"}, "correct_answer": "A"},
    {"id": 81, "difficulty": "hard", "question": "Number 1-100. Probability perfect square?", "options": {"A": "1/10", "B": "1/5", "C": "1/20", "D": "1/25"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Number 1-100. Probability prime?", "options": {"A": "1/4", "B": "1/5", "C": "1/6", "D": "1/3"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "If P(A)=1/4, P(B)=1/3, P(A∪B)=1/2, are A,B independent?", "options": {"A": "Yes", "B": "No", "C": "Cannot say", "D": "Sometimes"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If P(A)=0.2, P(B)=0.3, P(A∪B)=0.4, find P(A∩B)", "options": {"A": "0.1", "B": "0.06", "C": "0.5", "D": "0.14"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "P(A)=0.5, P(B)=0.6, P(A∩B)=0.3. Find P(neither A nor B)", "options": {"A": "0.2", "B": "0.3", "C": "0.4", "D": "0.1"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Cards: Probability of black card or queen?", "options": {"A": "7/13", "B": "1/2", "C": "15/26", "D": "8/13"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Cards: Probability of club or face card?", "options": {"A": "11/26", "B": "1/2", "C": "7/13", "D": "15/26"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "From word 'MATHEMATICS', probability of vowel?", "options": {"A": "4/11", "B": "3/11", "C": "5/11", "D": "7/11"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "From word 'PROBABILITY', probability of B?", "options": {"A": "2/11", "B": "1/11", "C": "1/6", "D": "2/13"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Month chosen randomly. Probability has 31 days?", "options": {"A": "7/12", "B": "1/2", "C": "5/12", "D": "2/3"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Bag: 5 red, 4 blue, 3 green. Three drawn. Probability all different colors?", "options": {"A": "3/11", "B": "2/11", "C": "4/11", "D": "5/11"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Bag: 6 red, 5 blue. Two drawn without replacement. Probability at least one red?", "options": {"A": "9/11", "B": "6/11", "C": "5/11", "D": "7/11"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Two dice rolled. Probability sum is perfect square?", "options": {"A": "7/36", "B": "1/6", "C": "5/36", "D": "1/9"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Two dice rolled. Probability sum is multiple of 4?", "options": {"A": "1/4", "B": "1/3", "C": "5/18", "D": "7/36"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Three coins tossed. Probability number of heads > number of tails?", "options": {"A": "1/2", "B": "3/8", "C": "1/4", "D": "5/8"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If P(A)=2x, P(B)=3x, P(A∪B)=5x, find x if A,B mutually exclusive", "options": {"A": "1/10", "B": "1/5", "C": "1/6", "D": "1/4"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "If P(A)=0.4, P(B)=0.5, P(A'∩B')=0.2, find P(A∩B)", "options": {"A": "0.1", "B": "0.2", "C": "0.3", "D": "0.4"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "A problem given to A,B independently. Probability A solves=1/2, B solves=1/3. Probability problem solved?", "options": {"A": "2/3", "B": "1/3", "C": "1/2", "D": "5/6"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Probability it rains Saturday is 0.6, Sunday is 0.7, both is 0.5. Probability it rains on at least one day?", "options": {"A": "0.8", "B": "0.9", "C": "0.7", "D": "0.4"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "If P(A)=0.3, P(B)=0.4, P(A|B)=0.5, find P(B|A)", "options": {"A": "2/3", "B": "1/3", "C": "1/2", "D": "3/4"}, "correct_answer": "A"}
  ]
}