2. What is the probability of rolling a sum of 8 when two fair six-sided dice are rolled?

4. A student answers 3 multiple-choice questions, each with 4 options. What is the probability of answering all 3 correctly by guessing?

5. In a class, 60% of students own a smartphone, 30% own a laptop, and 20% own both. What is the probability that a randomly selected student owns a smartphone OR a laptop?

1. A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?

8. A card is drawn from a standard 52-card deck. What is the probability that it is a King or a Spade?

9. A factory produces light bulbs, and 2% are defective. If a sample of 3 bulbs is randomly selected, what is the probability that none are defective?

10. What is the probability that a number chosen randomly from the integers 1 to 20 (inclusive) is a multiple of 3 or 5?

11. Two events A and B are mutually exclusive. If P(A) = 0.25 and P(B) = 0.4, what is P(A + B)?

12. If the probability of passing a driving test on any attempt is 0.7, what is the probability that someone only passes the test on the second attempt?

13. A bag contains 4 green, 5 yellow, and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that they are both green?

16. A fair die is rolled 5 times. What is the probability of getting at least one 6?

17. If P(A) = 0.5, P(B) = 0.6, and A and B are independent events, what is P(A + B)?

18. You draw two cards from a standard deck without replacement. What is the probability that the first is a King and the second is a Queen?

19. A spinner has sections labeled 1, 2, 3, 4, 5, all of equal size. If you spin it twice, what is the probability that the sum of the two spins is 6?

21. What is the probability of flipping a coin 5 times and getting exactly 2 tails?

22. Given P(X) = 0.8 and P(Y) = 0.7. If X and Y are independent, what is P(XY)?

23. From a batch of 15 batteries, 3 are defective. If 2 batteries are randomly selected, what is the probability that at least one is defective?

24. A student guesses on all 10 true/false questions on a quiz. What is the probability of getting exactly 7 correct?

26. If the probability of hitting a target is 0.4, what is the probability of hitting the target on the first shot and missing on the second?

27. Two bags contain some marbles. Bag A has 2 red, 3 blue. Bag B has 3 red, 1 blue. A bag is chosen at random and a marble is drawn. What is the probability that it is red?

28. What is the probability that in a group of 3 people, at least two share the same birth month? (Assume equal probability for all 12 months).

29. A multiple-choice test has 5 questions, each with 4 possible answers. If a student guesses on every question, what is the probability they get exactly 1 correct answer?

32. A box contains 10 items, of which 3 are defective. If 3 items are drawn without replacement, what is the probability that none are defective?

The probability of rain on Monday is 0.6. The probability of rain on Tuesday is 0.7. If the probability of rain on both days is 0.5, what is the probability it rains on neither day?

36. What is the probability of getting a sum of 9 or more when rolling two fair dice?

37. From a committee of 6 men and 4 women, a subcommittee of 3 is to be chosen. What is the probability that the subcommittee consists of 2 men and 1 woman?

40. A diagnostic test for a disease has a 95% accuracy rate (correctly identifies diseased or non-diseased). If 1% of the population has the disease, what is the probability a randomly selected person tests positive?

44. If P(A ∩ B) = 0.2 and P(A) = 0.5, what is P(B) given that A and B are independent events?

47. A archer hits the target 80% of the time. If they shoot 3 arrows, what is the probability they hit the target at least twice?

48. What is the probability that a 4-digit number formed using digits 1, 2, 3, 4 without repetition is divisible by 4?

51. How many distinct ways can the letters of the word "ARITHMETIC" be arranged?

52. In how many ways can 5 boys and 4 girls be seated in a row if the girls must sit together?

53. How many different 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition is not allowed and the number must be even?

54. A committee of 4 is to be chosen from 7 men and 5 women. How many ways can the committee be formed if it must consist of exactly 2 men and 2 women?

55. How many unique permutations are there of the letters in the word "STATISTICS"?

56. How many ways can 6 different books be arranged on a shelf if 3 particular books must always be together?

58. In how many ways can the letters of the word "ENGINEERING" be arranged?

60. How many different paths are there from point (0,0) to point (4,3) on a grid, moving only right or up?

61. How many ways can 5 distinct prizes be awarded to 3 students if each student can receive multiple prizes?

62. How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if repetition is allowed and the number must be greater than 300?

63. In how many ways can 7 people be seated around a circular table?

64. How many subsets can be formed from a set of 8 distinct elements?

65. From a standard 52-card deck, how many different 5-card hands are possible that contain exactly 3 Kings?

66. A student has 6 history books and 4 math books. In how many ways can they arrange 3 history books and 2 math books on a shelf?

67. How many distinct 5-digit numbers can be formed using the digits 1, 1, 2, 2, 3?

68. A group of 10 friends wants to play a game requiring teams of 3 and 7. How many ways can they form these two teams?

69. How many positive integers less than 1000 have digits that are all distinct?

70. How many ways can 4 married couples sit in a row if each couple must sit together?

72. If a true/false test has 10 questions, in how many ways can a student answer the test?

73. How many different committees of 5 can be formed from 9 people if one particular person must be on the committee?

75. In how many ways can 8 people be seated in a row if 3 specific people must sit next to each other?

76. How many different arrangements of the letters in "PROBABILITY" are there?

77. How many ways can 10 distinct items be divided into two groups of 6 and 4?

78. A coin is tossed 6 times. In how many sequences are there exactly 4 heads?

79. How many different straight lines can be formed by joining any two points from 7 points, no three of which are collinear?

80. How many different 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed?

81. From 5 mathematicians and 6 physicists, a committee of 4 is to be formed. How many ways can this be done if the committee must contain at least 2 mathematicians?

82. In how many ways can 3 blue and 4 red balls be arranged in a row?

84. How many ways can 5 boys and 5 girls be seated in a row if boys and girls must alternate?

85. How many different 5-card hands are possible that contain at least one King?

88. How many ways can a president, vice-president, secretary, and treasurer be chosen from a group of 10 people?

89. How many unique permutations are there of the letters in the word "PARALLEL"?

90. How many different ways can a student answer 5 questions on a 10-question exam if they must answer at least 3 questions from the first 5?

91. How many different committees of 3 can be formed from 12 people if two particular people cannot be on the same committee?

92. A set contains 5 elements. How many proper subsets does it have?

93. How many different 6-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if even digits must occupy even positions and odd digits must occupy odd positions?

97. How many different words can be formed by rearranging the letters of "CALCULUS"?

A class has 10 boys and 8 girls. A committee of 4 students is to be selected randomly. How many different committees of 4 students can be formed?

A class has 10 boys and 8 girls. A committee of 4 students is to be selected randomly. What is the probability that the committee consists of exactly 2 boys and 2 girls?

A class has 10 boys and 8 girls. A committee of 4 students is to be selected randomly. What is the probability that the committee consists of only girls?

A class has 10 boys and 8 girls. A committee of 4 students is to be selected randomly. What is the probability that the committee has at least one boy?

A standard 32-card Hungarian deck is shuffled. What is the probability of drawing a card that is either a King or any Red card?

In a class of 12 students, a 3-person committee is to be chosen. How many different ways can the committee be formed?

Using the digits {1, 2, 3, 4, 5} without repetition, how many different 3-digit numbers greater than 400 can be formed?

An urn contains 6 red and 4 blue balls. If you draw two balls without replacement, what is the probability that both balls are red?

An urn contains 6 red and 4 blue balls. If you draw two balls without replacement, what is the probability that you draw one of each colour?

Events A and B are independent. If P(A) = 0.3 and P(B) = 0.5, what is P(A + B)?

A basketball player has a 70% chance of making a free throw. He takes 5 free throws. What is the probability that he makes exactly 3 free throws?

A basketball player has a 70% chance of making a free throw. He takes 5 free throws. What is the probability that he makes at least 4 free throws?

A basketball player has a 70% chance of making a free throw. He takes 5 free throws. What is the probability that he makes none of the free throws?

A student is taking a multiple-choice quiz. Each question has 4 possible answers, and only one is correct. There are 5 questions on the quiz. The student guesses the answer to every question. What is the probability that the student gets exactly 3 questions correct?

A student is taking a multiple-choice quiz. Each question has 4 possible answers, and only one is correct. There are 5 questions on the quiz. The student guesses the answer to every question. What is the probability that the student gets at least 4 questions correct?

A student is taking a multiple-choice quiz. Each question has 4 possible answers, and only one is correct. There are 5 questions on the quiz. The student guesses the answer to every question. What is the probability that the student gets less than 2 questions correct?

A fair six-sided die is rolled 3 times. What is the probability of getting exactly two 5s?

A fair six-sided die is rolled 3 times. What is the probability of getting no 5s?

A drawer contains 5 loose socks: 2 are black and 3 are white. If you pull out 2 socks at random, what is the probability that you pull out a matching pair?

A box of chocolates has 7 pieces: 4 are dark chocolate and 3 are milk chocolate. If you pick 3 chocolates one by one without looking, what is the probability that you pick exactly 2 dark chocolates?

A committee of 3 people is to be chosen from a group of 5 men and 4 women. What is the probability that the committee consists of exactly 2 men and 1 woman?

A batch of 10 items contains 3 defective items and 7 non-defective items. An inspector selects 3 items from the batch without replacement. What is the probability that the third item selected is the first defective item found?