{
  "title": "Complementary Events - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "If P(A) = 0.7, then P(not A) = ?", "options": {"A": "0.3", "B": "0.7", "C": "0.4", "D": "0.5"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "The sum of probabilities of an event and its complement is always:", "options": {"A": "0", "B": "0.5", "C": "1", "D": "2"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "If P(E) = 0.05, then P(not E) = ?", "options": {"A": "0.95", "B": "0.05", "C": "0.5", "D": "0.005"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "The complement of event 'getting a head' in coin toss is:", "options": {"A": "Getting a tail", "B": "Getting head again", "C": "Getting no toss", "D": "Getting both"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "If P(rain) = 0.3, then P(no rain) = ?", "options": {"A": "0.7", "B": "0.3", "C": "0.5", "D": "0.03"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "For any event A, P(A) + P(A') = ?", "options": {"A": "0", "B": "0.5", "C": "1", "D": "2"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "If P(pass) = 0.8, then P(fail) = ?", "options": {"A": "0.2", "B": "0.8", "C": "0.1", "D": "0.5"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "The complement of 'winning' is:", "options": {"A": "Losing", "B": "Winning again", "C": "Not playing", "D": "Tie"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "If P(success) = 0.65, then P(not success) = ?", "options": {"A": "0.35", "B": "0.65", "C": "0.45", "D": "0.55"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "P(A') = 1 - ?", "options": {"A": "P(A)", "B": "P(B)", "C": "0", "D": "1"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "If probability of an event is 1, probability of its complement is:", "options": {"A": "0", "B": "1", "C": "0.5", "D": "2"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Complement of 'drawing a red card' from deck is:", "options": {"A": "Drawing a black card", "B": "Drawing a heart", "C": "Drawing any card", "D": "Not drawing"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If P(A) = 0, then P(A') = ?", "options": {"A": "1", "B": "0", "C": "0.5", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "For a sure event, probability of its complement is:", "options": {"A": "0", "B": "1", "C": "0.5", "D": "0.75"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "If P(event) = 0.25, then P(complement) = ?", "options": {"A": "0.75", "B": "0.25", "C": "0.5", "D": "0.125"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Complement of 'rolling an even number' on die is:", "options": {"A": "Rolling an odd number", "B": "Rolling 1", "C": "Rolling 6", "D": "Not rolling"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "If P(A) = 0.99, then P(A') = ?", "options": {"A": "0.01", "B": "0.99", "C": "0.1", "D": "0.09"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "For impossible event, probability of complement is:", "options": {"A": "1", "B": "0", "C": "0.5", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If P(rain tomorrow) = 0.4, then P(no rain tomorrow) = ?", "options": {"A": "0.6", "B": "0.4", "C": "0.2", "D": "0.8"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "P(A) and P(A') are always:", "options": {"A": "Equal", "B": "Add to 1", "C": "Add to 0", "D": "Independent"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "If P(A) = 2/3, then P(A') = ?", "options": {"A": "1/3", "B": "2/3", "C": "3/2", "D": "1/2"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "A and A' are mutually exclusive and:", "options": {"A": "Exhaustive", "B": "Independent", "C": "Equal", "D": "Overlapping"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "If P(A') = 0.37, then P(A) = ?", "options": {"A": "0.63", "B": "0.37", "C": "0.73", "D": "0.27"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "For two complementary events A and B, P(A) + P(B) = ?", "options": {"A": "1", "B": "0", "C": "0.5", "D": "2"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If P(A) = 0.83, find P(A') correct to two decimal places.", "options": {"A": "0.17", "B": "0.83", "C": "0.16", "D": "0.18"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "The complement of 'getting at least one head' in two coin tosses is:", "options": {"A": "Getting no heads", "B": "Getting two heads", "C": "Getting one head", "D": "Getting two tails"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If P(E) = 3/8, then P(not E) = ?", "options": {"A": "5/8", "B": "3/8", "C": "8/3", "D": "1/8"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "P(A) = 0.6, P(B) = 0.3, if A and B are complementary, is this possible?", "options": {"A": "No, sum ≠ 1", "B": "Yes", "C": "Maybe", "D": "Only if independent"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Complement of 'getting a prime number' on a die is:", "options": {"A": "Getting 1,4,6", "B": "Getting 2,3,5", "C": "Getting odd numbers", "D": "Getting even numbers"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If P(A') = 7/10, then P(A) = ?", "options": {"A": "3/10", "B": "7/10", "C": "10/7", "D": "10/3"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "For event E, P(E) + P(not E) always equals:", "options": {"A": "1", "B": "0", "C": "Between 0 and 1", "D": "2"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If P(A) = 0.45 and P(B) = 0.55, and A and B are complementary, then:", "options": {"A": "B = A'", "B": "A and B independent", "C": "A and B mutually exclusive but not exhaustive", "D": "Sum is 1, so yes complementary"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "The complement of 'drawing a face card' from deck is:", "options": {"A": "Drawing a non-face card", "B": "Drawing an ace", "C": "Drawing number card", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "If P(A) = p, then P(A') = ?", "options": {"A": "1-p", "B": "p", "C": "p-1", "D": "1/p"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "For complementary events, which is true?", "options": {"A": "They cover all possibilities", "B": "They cannot occur together", "C": "Sum of probabilities = 1", "D": "All of these"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "If P(A) = 0.72, then P(A') to nearest hundredth is:", "options": {"A": "0.28", "B": "0.27", "C": "0.73", "D": "0.72"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Complement of 'getting sum ≥ 10' with two dice is:", "options": {"A": "Getting sum ≤ 9", "B": "Getting sum < 10", "C": "Getting sum = 10", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 38, "difficulty": "medium", "question": "If P(A') = 0.009, then P(A) = ?", "options": {"A": "0.991", "B": "0.009", "C": "0.99", "D": "0.91"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "A and A' are always:", "options": {"A": "Mutually exclusive and exhaustive", "B": "Independent", "C": "Equally likely", "D": "Overlapping"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If P(A) = 5/6, then P(not A) = ?", "options": {"A": "1/6", "B": "5/6", "C": "6/5", "D": "1/5"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "The complement of 'selecting a boy' from a group is:", "options": {"A": "Selecting a girl", "B": "Not selecting", "C": "Selecting either", "D": "Selecting both"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If P(A) = 0.01, then P(A') = ?", "options": {"A": "0.99", "B": "0.01", "C": "0.1", "D": "0.9"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "For event E, P(E) = 1 - P(?)", "options": {"A": "E'", "B": "E", "C": "Sample space", "D": "None"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "If P(rain) = 0.35, P(no rain) = ?", "options": {"A": "0.65", "B": "0.35", "C": "0.7", "D": "0.3"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "The complement of 'winning first prize' is:", "options": {"A": "Not winning first prize", "B": "Winning second prize", "C": "Losing", "D": "All except first prize"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "If P(A) = 0.999, then P(A') = ?", "options": {"A": "0.001", "B": "0.999", "C": "0.01", "D": "0.1"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "A and A' together form the:", "options": {"A": "Sample space", "B": "Empty set", "C": "Universal set", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "If P(A) = 7/9, then P(A') = ?", "options": {"A": "2/9", "B": "7/9", "C": "9/7", "D": "9/2"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Complement of 'getting a red or black card' from deck is:", "options": {"A": "Empty event", "B": "Getting joker", "C": "Getting no card", "D": "Impossible event"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "medium", "question": "If P(A) = 0, then A and A' are:", "options": {"A": "Complementary", "B": "Not complementary", "C": "Same", "D": "Independent"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "If P(A) = 1/4, then P(A') = ?", "options": {"A": "3/4", "B": "1/4", "C": "4", "D": "1/3"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "The complement of 'rolling a number > 4' on die is:", "options": {"A": "Rolling number ≤ 4", "B": "Rolling 1,2,3,4", "C": "Both A and B", "D": "Rolling 5,6 only"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "If P(E) = 0.125, then P(not E) = ?", "options": {"A": "0.875", "B": "0.125", "C": "0.25", "D": "0.5"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "For complementary events, P(A ∩ A') = ?", "options": {"A": "0", "B": "1", "C": "0.5", "D": "P(A)"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If P(A') = 0.2, then P(A) = ?", "options": {"A": "0.8", "B": "0.2", "C": "0.4", "D": "0.6"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Complement of 'selecting a vowel' from alphabet is:", "options": {"A": "Selecting a consonant", "B": "Selecting letter", "C": "Not selecting", "D": "Selecting any"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "If P(A) = 11/13, then P(A') = ?", "options": {"A": "2/13", "B": "11/13", "C": "13/11", "D": "13/2"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "For any event E, maximum value of P(E) + P(E') is:", "options": {"A": "1", "B": "2", "C": "0", "D": "∞"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "If P(A) = 0.375, then P(A') = ?", "options": {"A": "0.625", "B": "0.375", "C": "0.725", "D": "0.275"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "The complement of 'getting same outcome' on two coins is:", "options": {"A": "Getting different outcomes", "B": "Getting HH or TT", "C": "Getting HT or TH", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "If P(A') = 3/7, then P(A) = ?", "options": {"A": "4/7", "B": "3/7", "C": "7/3", "D": "7/4"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "For complementary events A and B, P(A ∪ B) = ?", "options": {"A": "1", "B": "0", "C": "P(A)+P(B)", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 63, "difficulty": "medium", "question": "If P(A) = 0.08, then P(A') = ?", "options": {"A": "0.92", "B": "0.08", "C": "0.18", "D": "0.82"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Complement of 'drawing a spade' from deck is:", "options": {"A": "Drawing heart, club, or diamond", "B": "Drawing black card", "C": "Drawing red card", "D": "Both A and C"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "If P(A) = 0.6 and P(B) = 0.4, and A and B complementary, then:", "options": {"A": "B = A'", "B": "This is possible", "C": "Both A and B", "D": "Not possible as sum=1"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "For event E, if P(E) = x, then P(E') = ?", "options": {"A": "1-x", "B": "x", "C": "x-1", "D": "1/x"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "If P(A') = 0.01, then P(A) = ?", "options": {"A": "0.99", "B": "0.01", "C": "0.1", "D": "0.9"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "The complement of 'getting at most 2 heads' in 3 coin tosses is:", "options": {"A": "Getting 3 heads", "B": "Getting more than 2 heads", "C": "Both A and B", "D": "Getting 0 heads"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "If P(A) = 9/10, then P(A') = ?", "options": {"A": "1/10", "B": "9/10", "C": "10/9", "D": "10/1"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "For complementary events, P(A) + P(A') always equals:", "options": {"A": "1", "B": "0.5", "C": "0", "D": "2"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "If P(A) = 0.44, then P(A') = ?", "options": {"A": "0.56", "B": "0.44", "C": "0.46", "D": "0.54"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Complement of 'selecting a multiple of 3' from 1 to 20 is:", "options": {"A": "Selecting non-multiples of 3", "B": "Selecting numbers not divisible by 3", "C": "Both A and B", "D": "Selecting 1,2,4,5,..."}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "If P(A') = 0.75, then P(A) = ?", "options": {"A": "0.25", "B": "0.75", "C": "0.5", "D": "0.3"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "The complement of an impossible event is:", "options": {"A": "Sure event", "B": "Impossible event", "C": "Equally likely", "D": "Independent event"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "If P(A) = 0.5, then P(A') = ?", "options": {"A": "0.5", "B": "1", "C": "0", "D": "0.25"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Complement of 'drawing a king' from deck is:", "options": {"A": "Drawing a non-king", "B": "Drawing any other card", "C": "Both A and B", "D": "Drawing queen or jack"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If P(A) = 1/8, then P(A') = ?", "options": {"A": "7/8", "B": "1/8", "C": "8", "D": "1/7"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "For event A, P(A) and P(A') are related as:", "options": {"A": "P(A') = 1 - P(A)", "B": "P(A) = 1 - P(A')", "C": "Both A and B", "D": "None"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "If P(A) = 0.33 (approx), then P(A') ≈ ?", "options": {"A": "0.67", "B": "0.33", "C": "0.77", "D": "0.23"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "The complement of 'getting sum 7' with two dice is:", "options": {"A": "Getting sum ≠ 7", "B": "Getting any other sum", "C": "Both A and B", "D": "Getting 2,3,4,5,6,8,9,10,11,12"}, "correct_answer": "C"},

    {"id": 81, "difficulty": "hard", "question": "If P(A) = 0.4 and P(B) = 0.7, can A and B be complementary?", "options": {"A": "No, sum ≠ 1", "B": "Yes, if overlapping", "C": "Yes, if independent", "D": "Yes, if mutually exclusive"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "For three events A,B,C that are mutually exclusive and exhaustive, P(A)+P(B)+P(C)=1. If C = (A∪B)', then:", "options": {"A": "C is complement of A∪B", "B": "P(C)=1-P(A)-P(B)", "C": "Both A and B", "D": "C is complement of A∩B"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "If P(A') = 3P(A), find P(A).", "options": {"A": "0.25", "B": "0.75", "C": "0.5", "D": "0.33"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "The complement of 'at least one' is:", "options": {"A": "None", "B": "All", "C": "Exactly one", "D": "At most one"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "If P(A) = 2P(A'), find P(A).", "options": {"A": "2/3", "B": "1/3", "C": "1/2", "D": "2/5"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "For events A and B, if A∪B = S (sample space) and A∩B = ∅, then B is complement of A only if:", "options": {"A": "Always true", "B": "Only if P(A)+P(B)=1", "C": "Only if equally likely", "D": "Never true"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "If P(A) + P(B) = 1 and A∩B = ∅, then B = A'?", "options": {"A": "Yes", "B": "No, need A∪B=S", "C": "Only if P(A)≠0", "D": "Only if independent"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "The complement of 'exactly two heads' in three tosses is:", "options": {"A": "0,1, or 3 heads", "B": "Not exactly two heads", "C": "Both A and B", "D": "0 or 3 heads"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "If P(A') = 4P(A), find P(A).", "options": {"A": "0.2", "B": "0.8", "C": "0.25", "D": "0.5"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "For event E, if P(E) = 0.3, then P(E'') = ? (where E'' = complement of complement)", "options": {"A": "0.3", "B": "0.7", "C": "0", "D": "1"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "If A and B are complementary and P(A) = 0.4, then P(A' ∩ B') = ?", "options": {"A": "0", "B": "0.4", "C": "0.6", "D": "1"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "The complement of 'more than 3' is:", "options": {"A": "3 or less", "B": "Less than 3", "C": "At most 3", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 93, "difficulty": "hard", "question": "If P(A) = 0.6 and P(B) = 0.5, and A and B are complementary, is this possible?", "options": {"A": "No, sum ≠ 1", "B": "Yes, if overlapping", "C": "Yes, if P(A∩B)=0.1", "D": "No, always impossible"}, "correct_answer": "D"},
    {"id": 94, "difficulty": "hard", "question": "If P(A) = 1 - P(B), then B is complement of A only when:", "options": {"A": "A∩B=∅", "B": "A∪B=S", "C": "Both A and B", "D": "Always"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "The complement of 'all heads' in n coin tosses is:", "options": {"A": "At least one tail", "B": "Not all heads", "C": "Both A and B", "D": "All tails"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "If P(A') = P(A) + 0.2, find P(A).", "options": {"A": "0.4", "B": "0.6", "C": "0.5", "D": "0.3"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "For events A and B, if B = A', then P(A|B) = ?", "options": {"A": "0", "B": "1", "C": "P(A)", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "The complement of 'neither A nor B' is:", "options": {"A": "A or B", "B": "At least one of A or B", "C": "Both A and B", "D": "Both A and B correct"}, "correct_answer": "D"},
    {"id": 99, "difficulty": "hard", "question": "If P(A) : P(A') = 3:2, find P(A).", "options": {"A": "0.6", "B": "0.4", "C": "0.5", "D": "3/5"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "For complementary events A and A', P(A ∪ A') - P(A ∩ A') = ?", "options": {"A": "1", "B": "0", "C": "P(A)", "D": "P(A')"}, "correct_answer": "A"}
  ]
}