{
  "title": "Simple Problems Based on Probability - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A coin is tossed once. Probability of getting head is:", "options": {"A": "1/2", "B": "1", "C": "0", "D": "1/4"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "A die is thrown. Probability of getting 3 is:", "options": {"A": "1/6", "B": "1/3", "C": "1/2", "D": "5/6"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "From deck of 52 cards, probability of drawing a king is:", "options": {"A": "1/13", "B": "4/13", "C": "1/52", "D": "1/4"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "A bag has 3 red, 5 blue balls. Probability of drawing red ball is:", "options": {"A": "3/8", "B": "5/8", "C": "3/5", "D": "5/3"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Probability of impossible event is:", "options": {"A": "0", "B": "1", "C": "1/2", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Probability of sure event is:", "options": {"A": "1", "B": "0", "C": "1/2", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Two coins tossed. Probability of at least one head:", "options": {"A": "3/4", "B": "1/4", "C": "1/2", "D": "1"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "A die thrown. Probability of even number:", "options": {"A": "1/2", "B": "1/3", "C": "2/3", "D": "1/6"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Probability of getting 7 on a die is:", "options": {"A": "0", "B": "1", "C": "1/6", "D": "1/7"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Month chosen randomly, probability it has 31 days:", "options": {"A": "7/12", "B": "1/2", "C": "5/12", "D": "31/365"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Card drawn from deck, probability of a heart:", "options": {"A": "1/4", "B": "1/13", "C": "1/52", "D": "13/52"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Probability that sun rises from west:", "options": {"A": "0", "B": "1", "C": "1/2", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "One card drawn, probability of black queen:", "options": {"A": "1/26", "B": "1/13", "C": "2/13", "D": "1/52"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Bag: 4 white, 3 black balls. Probability of white:", "options": {"A": "4/7", "B": "3/7", "C": "4/3", "D": "3/4"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Probability of getting a prime number on die:", "options": {"A": "1/2", "B": "2/3", "C": "1/3", "D": "5/6"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Two coins tossed, probability of two heads:", "options": {"A": "1/4", "B": "1/2", "C": "3/4", "D": "1"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Probability of getting number > 6 on die:", "options": {"A": "0", "B": "1", "C": "1/6", "D": "5/6"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Day chosen randomly, probability it's Sunday:", "options": {"A": "1/7", "B": "7", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Card drawn, probability not a king:", "options": {"A": "12/13", "B": "1/13", "C": "4/13", "D": "1/4"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Probability ranges between:", "options": {"A": "0 and 1", "B": "-1 and 1", "C": "0 and 100", "D": "0 and ∞"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Two dice thrown. Probability sum = 7:", "options": {"A": "1/6", "B": "1/12", "C": "7/36", "D": "5/36"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Bag: 5 red, 7 green balls. Two drawn together, probability both red:", "options": {"A": "5/33", "B": "25/144", "C": "5/12", "D": "7/33"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Card drawn, probability either king or queen:", "options": {"A": "2/13", "B": "1/13", "C": "4/13", "D": "8/13"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Three coins tossed. Probability exactly two heads:", "options": {"A": "3/8", "B": "1/8", "C": "1/2", "D": "5/8"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Two dice thrown. Probability doublet:", "options": {"A": "1/6", "B": "1/36", "C": "1/12", "D": "5/36"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Bag: 8 red, 6 blue. One ball drawn, probability not blue:", "options": {"A": "4/7", "B": "3/7", "C": "6/14", "D": "8/14"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Card drawn, probability spade or ace:", "options": {"A": "4/13", "B": "1/13", "C": "17/52", "D": "16/52"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Two dice thrown. Probability sum > 10:", "options": {"A": "1/12", "B": "1/6", "C": "5/36", "D": "1/18"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Probability that leap year has 53 Sundays:", "options": {"A": "2/7", "B": "1/7", "C": "52/366", "D": "53/366"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Bag: 3 red, 4 blue, 5 green. One ball drawn, probability not green:", "options": {"A": "7/12", "B": "5/12", "C": "1/3", "D": "2/3"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Two dice thrown. Probability sum prime number:", "options": {"A": "5/12", "B": "1/3", "C": "7/36", "D": "15/36"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "Card drawn, probability neither red nor queen:", "options": {"A": "6/13", "B": "7/13", "C": "1/2", "D": "11/26"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Three coins tossed. Probability at least one tail:", "options": {"A": "7/8", "B": "1/8", "C": "3/8", "D": "1/2"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Two dice thrown. Probability sum divisible by 3:", "options": {"A": "1/3", "B": "1/6", "C": "1/2", "D": "2/3"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Bag: 6 white, 4 black. Two balls drawn without replacement, probability both white:", "options": {"A": "1/3", "B": "2/3", "C": "3/5", "D": "9/25"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Card drawn, probability face card (J,Q,K):", "options": {"A": "3/13", "B": "1/13", "C": "4/13", "D": "12/13"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Two dice thrown. Probability sum even:", "options": {"A": "1/2", "B": "1/4", "C": "3/4", "D": "2/3"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Probability that non-leap year has 53 Sundays:", "options": {"A": "1/7", "B": "2/7", "C": "52/365", "D": "53/365"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Bag: 5 red, 3 blue, 2 green. One ball drawn, probability red or green:", "options": {"A": "7/10", "B": "1/2", "C": "3/5", "D": "2/5"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Two coins tossed. Probability at most one head:", "options": {"A": "3/4", "B": "1/4", "C": "1/2", "D": "1"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Die thrown twice. Probability same number both times:", "options": {"A": "1/6", "B": "1/36", "C": "1/12", "D": "5/36"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Card drawn, probability not a face card:", "options": {"A": "10/13", "B": "3/13", "C": "1/13", "D": "12/13"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Two dice thrown. Probability sum ≤ 5:", "options": {"A": "5/18", "B": "1/6", "C": "5/36", "D": "10/36"}, "correct_answer": "D"},
    {"id": 44, "difficulty": "medium", "question": "Bag: 4 red, 5 blue. Two balls drawn with replacement, probability both red:", "options": {"A": "16/81", "B": "4/9", "C": "1/6", "D": "4/5"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Probability month starts with Sunday in non-leap year:", "options": {"A": "1/7", "B": "12/365", "C": "52/365", "D": "2/7"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Two dice thrown. Probability product 12:", "options": {"A": "1/9", "B": "1/12", "C": "1/18", "D": "1/36"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Card drawn, probability black or king:", "options": {"A": "7/13", "B": "6/13", "C": "1/2", "D": "8/13"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Three coins tossed. Probability at most two heads:", "options": {"A": "7/8", "B": "3/8", "C": "1/8", "D": "1/2"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Two dice thrown. Probability sum 8 or 9:", "options": {"A": "5/18", "B": "1/6", "C": "5/36", "D": "7/36"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Bag: 3 red, 4 blue, x green. P(red)=1/5. Find x.", "options": {"A": "8", "B": "7", "C": "6", "D": "5"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Two dice thrown. Probability difference 2:", "options": {"A": "2/9", "B": "1/6", "C": "5/18", "D": "1/9"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Card drawn, probability neither ace nor spade:", "options": {"A": "9/13", "B": "4/13", "C": "10/13", "D": "1/2"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Three coins tossed. Probability exactly one head:", "options": {"A": "3/8", "B": "1/8", "C": "1/2", "D": "5/8"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Two dice thrown. Probability sum multiple of 4:", "options": {"A": "1/4", "B": "1/3", "C": "5/36", "D": "1/6"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Bag: 6 white, 9 black. Two drawn without replacement, probability different colors:", "options": {"A": "18/35", "B": "9/35", "C": "12/35", "D": "6/35"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Card drawn, probability number card (2-10):", "options": {"A": "9/13", "B": "10/13", "C": "3/13", "D": "1/2"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Two dice thrown. Probability sum odd:", "options": {"A": "1/2", "B": "1/4", "C": "3/4", "D": "2/3"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Probability randomly chosen two digit number divisible by 5:", "options": {"A": "1/5", "B": "9/89", "C": "18/90", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "medium", "question": "Bag: 4 red, 6 blue. Two drawn, probability at least one red:", "options": {"A": "2/3", "B": "1/3", "C": "4/15", "D": "11/15"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Two coins tossed. Probability exactly one tail:", "options": {"A": "1/2", "B": "1/4", "C": "3/4", "D": "1"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Die thrown twice. Probability first > second:", "options": {"A": "5/12", "B": "1/2", "C": "1/6", "D": "5/6"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Card drawn, probability diamond or face card:", "options": {"A": "11/26", "B": "1/2", "C": "7/13", "D": "25/52"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Two dice thrown. Probability sum 6 or 11:", "options": {"A": "7/36", "B": "1/6", "C": "5/36", "D": "1/9"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Bag: 5 red, 3 blue, 2 green. Two drawn without replacement, probability both same color:", "options": {"A": "14/45", "B": "19/45", "C": "2/9", "D": "1/3"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Probability random two digit number divisible by 7:", "options": {"A": "13/90", "B": "7/45", "C": "1/7", "D": "14/99"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Two dice thrown. Probability sum 10 given first die shows 4:", "options": {"A": "1/6", "B": "1/12", "C": "1/36", "D": "0"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Card drawn, probability red face card:", "options": {"A": "3/26", "B": "3/13", "C": "1/13", "D": "6/52"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Three coins tossed. Probability all same:", "options": {"A": "1/4", "B": "3/8", "C": "1/2", "D": "1/8"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Two dice thrown. Probability sum ≥ 9:", "options": {"A": "5/18", "B": "1/6", "C": "7/36", "D": "10/36"}, "correct_answer": "D"},
    {"id": 70, "difficulty": "medium", "question": "Bag: 8 red, 5 blue. Three drawn, probability all red:", "options": {"A": "28/143", "B": "5/143", "C": "56/429", "D": "8/13"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Probability number from 1-100 divisible by 6 or 8:", "options": {"A": "1/4", "B": "6/25", "C": "12/100", "D": "24/100"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Two dice thrown. Probability sum prime or even:", "options": {"A": "5/6", "B": "2/3", "C": "1/2", "D": "3/4"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Card drawn, probability not diamond:", "options": {"A": "3/4", "B": "1/4", "C": "13/52", "D": "39/52"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Three coins tossed. Probability at least two tails:", "options": {"A": "1/2", "B": "3/8", "C": "1/8", "D": "5/8"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Two dice thrown. Probability product odd:", "options": {"A": "1/4", "B": "1/2", "C": "3/4", "D": "1/8"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Bag: 7 red, 4 blue. Two drawn with replacement, probability different colors:", "options": {"A": "56/121", "B": "28/121", "C": "49/121", "D": "16/121"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Probability number from 1-50 divisible by 4:", "options": {"A": "12/50", "B": "6/25", "C": "1/4", "D": "All correct"}, "correct_answer": "D"},
    {"id": 78, "difficulty": "medium", "question": "Two dice thrown. Probability sum 5 given first die shows 2:", "options": {"A": "1/6", "B": "1/12", "C": "1/36", "D": "4/36"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Card drawn, probability heart or ace:", "options": {"A": "4/13", "B": "1/4", "C": "17/52", "D": "16/52"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Three coins tossed. Probability number of heads even:", "options": {"A": "1/2", "B": "3/8", "C": "5/8", "D": "1/4"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Two cards drawn from deck without replacement. Probability both aces:", "options": {"A": "1/221", "B": "1/13", "C": "4/663", "D": "1/52"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Three dice thrown. Probability sum 15:", "options": {"A": "5/108", "B": "1/36", "C": "10/216", "D": "5/72"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "Bag: 5 red, 4 blue. Three drawn, probability exactly two red:", "options": {"A": "10/21", "B": "5/14", "C": "40/84", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 84, "difficulty": "hard", "question": "Probability that among 3 persons, at least 2 have same birthday (ignore leap):", "options": {"A": "≈0.0082", "B": "≈0.008", "C": "1 - (365×364×363)/(365³)", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "Two cards drawn, probability one king and one queen:", "options": {"A": "8/663", "B": "4/663", "C": "16/663", "D": "32/663"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Three dice thrown. Probability all different numbers:", "options": {"A": "5/9", "B": "1/36", "C": "120/216", "D": "5/54"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Bag: 6 white, 4 red. Three drawn, probability at least one red:", "options": {"A": "5/6", "B": "1/6", "C": "29/30", "D": "1/30"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Four coins tossed. Probability exactly three heads:", "options": {"A": "1/4", "B": "1/2", "C": "3/8", "D": "1/8"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Two cards drawn without replacement, probability both same suit:", "options": {"A": "4/17", "B": "1/4", "C": "12/51", "D": "13/51"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Three dice thrown. Probability sum 10:", "options": {"A": "1/8", "B": "27/216", "C": "3/216", "D": "27/216"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "Bag: 3 red, 5 blue, 2 green. Three drawn, probability all different colors:", "options": {"A": "3/10", "B": "1/4", "C": "1/2", "D": "2/5"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Five coins tossed. Probability at least 3 heads:", "options": {"A": "1/2", "B": "13/16", "C": "5/16", "D": "11/16"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Two cards drawn without replacement, probability one is spade king:", "options": {"A": "1/26", "B": "1/52", "C": "50/663", "D": "1/663"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Three dice thrown. Probability at least one 6:", "options": {"A": "91/216", "B": "125/216", "C": "1/216", "D": "5/72"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Bag: 4 red, 5 blue, 6 green. Three drawn, probability exactly two green:", "options": {"A": "135/455", "B": "27/91", "C": "15/91", "D": "5/14"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Four coins tossed. Probability number of heads ≥ number of tails:", "options": {"A": "11/16", "B": "1/2", "C": "5/8", "D": "3/8"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Two cards drawn without replacement, probability both face cards:", "options": {"A": "11/221", "B": "1/221", "C": "9/221", "D": "12/221"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Three dice thrown. Probability sum divisible by 3:", "options": {"A": "1/3", "B": "1/2", "C": "2/3", "D": "1/4"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Bag: 2 red, 3 blue, 4 green. Three drawn, probability at least one red:", "options": {"A": "7/12", "B": "5/12", "C": "37/42", "D": "5/42"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Five coins tossed. Probability exactly two tails:", "options": {"A": "5/16", "B": "1/4", "C": "10/32", "D": "Both A and C"}, "correct_answer": "D"}
  ]
}