[ { "Question": "What is the probability of rolling a 4 on a fair six-sided die?", "Answer": "B", "Explanation": "There is only one favorable outcome (rolling a 4) out of 6 possible outcomes, so the probability is 1/6.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/1/1b/Dice-6.svg", "OptionA": "1/4", "OptionB": "1/6", "OptionC": "1/3", "OptionD": "1/2", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 1, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "If you flip a fair coin twice, what is the total number of possible outcomes?", "Answer": "C", "Explanation": "Each flip has 2 possible outcomes, so total outcomes = 2 × 2 = 4.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/8/8d/Coins_icon.svg", "OptionA": "2", "OptionB": "3", "OptionC": "4", "OptionD": "6", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 2, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "How many different 3-letter arrangements can be made from the letters A, B, and C if repetition is allowed?", "Answer": "D", "Explanation": "Each position can be any of the 3 letters, so total arrangements = 3 × 3 × 3 = 27.", "PictureURL": "", "OptionA": "6", "OptionB": "9", "OptionC": "18", "OptionD": "27", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 3, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "What is the probability of drawing a red card from a standard deck of 52 cards?", "Answer": "A", "Explanation": "Half the cards (26) are red (hearts and diamonds), so probability = 26/52 = 1/2.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/5/57/Playing_card_heart_A.svg", "OptionA": "1/2", "OptionB": "1/4", "OptionC": "1/13", "OptionD": "1/26", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 4, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "How many ways can you arrange the letters in the word 'CAT'?", "Answer": "B", "Explanation": "There are 3 letters, so the number of arrangements is 3! = 3 × 2 × 1 = 6.", "PictureURL": "", "OptionA": "3", "OptionB": "6", "OptionC": "9", "OptionD": "12", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 5, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "If you roll two six-sided dice, what is the probability that the sum is 7?", "Answer": "C", "Explanation": "There are 6 favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total outcomes, so probability = 6/36 = 1/6.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/1/1b/Dice-6.svg", "OptionA": "1/12", "OptionB": "1/36", "OptionC": "1/6", "OptionD": "1/3", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 6, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "How many different 2-digit numbers can be formed using digits 1, 2, 3, and 4 without repetition?", "Answer": "B", "Explanation": "For the first digit, 4 choices; for the second digit, 3 choices (no repetition), total = 4 × 3 = 12.", "PictureURL": "", "OptionA": "8", "OptionB": "12", "OptionC": "16", "OptionD": "24", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 7, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "What is the probability of drawing an ace from a standard deck of 52 cards?", "Answer": "D", "Explanation": "There are 4 aces in the deck, so probability = 4/52 = 1/13.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/5/57/Playing_card_spade_A.svg", "OptionA": "1/4", "OptionB": "1/52", "OptionC": "1/26", "OptionD": "1/13", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 8, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "If you have 5 different books, in how many ways can you arrange them on a shelf?", "Answer": "A", "Explanation": "Number of arrangements is 5! = 5 × 4 × 3 × 2 × 1 = 120.", "PictureURL": "", "OptionA": "120", "OptionB": "25", "OptionC": "60", "OptionD": "10", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 9, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "What is the probability of getting heads exactly once when flipping a fair coin three times?", "Answer": "B", "Explanation": "Number of ways to get exactly one head is 3 (HTT, THT, TTH). Total outcomes = 8. Probability = 3/8.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/8/8d/Coins_icon.svg", "OptionA": "1/8", "OptionB": "3/8", "OptionC": "1/2", "OptionD": "1/4", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 10, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "How many different license plates can be made if a plate has 3 letters followed by 2 digits, letters and digits can repeat?", "Answer": "C", "Explanation": "Letters: 26 choices each, digits: 10 choices each. Total = 26^3 × 10^2 = 175,760.", "PictureURL": "", "OptionA": "676,000", "OptionB": "17,576", "OptionC": "1,757,600", "OptionD": "175,760", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 11, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "If you randomly select one card from a deck, what is the probability it is a face card (Jack, Queen, or King)?", "Answer": "D", "Explanation": "There are 12 face cards (3 per suit × 4 suits), so probability = 12/52 = 3/13.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/9/9a/Playing_card_jack_of_spades.svg", "OptionA": "1/13", "OptionB": "1/4", "OptionC": "1/3", "OptionD": "3/13", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 12, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "How many ways can you choose 2 toppings from 5 available toppings for a pizza if order does not matter?", "Answer": "B", "Explanation": "Number of combinations is C(5,2) = 5!/(2!×3!) = 10.", "PictureURL": "", "OptionA": "20", "OptionB": "10", "OptionC": "15", "OptionD": "25", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 13, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "What is the probability of drawing a queen or a heart from a standard deck of 52 cards?", "Answer": "C", "Explanation": "Queens: 4 cards, Hearts: 13 cards, Queen of hearts counted twice, so total favorable = 4 + 13 - 1 = 16. Probability = 16/52 = 4/13.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/5/57/Playing_card_heart_Q.svg", "OptionA": "1/4", "OptionB": "3/13", "OptionC": "4/13", "OptionD": "1/2", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 14, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" }, { "Question": "If you roll one six-sided die, what is the probability of rolling an even number?", "Answer": "B", "Explanation": "Even numbers on a die are 2, 4, and 6, so 3 favorable outcomes out of 6 total, probability = 3/6 = 1/2.", "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/1/1b/Dice-6.svg", "OptionA": "1/3", "OptionB": "1/2", "OptionC": "1/6", "OptionD": "2/3", "OptionE": "", "OptionF": "", "OptionG": "", "TestName": "Probability and Counting Principles Practice Test", "Content Type": "multiple choice", "Title": "Probability – simple events, counting principles", "Item": 15, "Type": "multiple choice", "Path": "Subtopics: — Probability – simple events, counting principles" } ]