1. A box contains 4 red and 6 black balls. What is the probability of picking a red ball?
2. A jar contains exactly 5 red marbles, 4 blue marbles, and 3 yellow marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles drawn will be the same color?
3. Events A and B are mutually exclusive. $P(A) = 0.5$ and $P(B) = 0.3$. What is $P(A \text{ or } B)$?
4. In a carnival game, rolling an even number wins \$4.00 and rolling odd loses \$2.00. What is the expected value of a single roll?
5. A local arcade has a prize wheel with 4 colored sections. The table shows the results over 200 spins. To make each color exactly 25%, which change is the best fix?
6. Whole numbers 1 through 20 are placed in a hat. One slip is drawn at random. What is the probability that the number is a multiple of 3?
7. A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting heads and rolling an even number? (Assume the events are independent.)
8. If an event occurs with a probability of 0.25, what is the probability of the event not occurring?
9. A jar contains 4 white balls and 6 black balls. Two balls are drawn <u>without replacement</u>. What is the probability that both balls are white?
10. If an event occurs with probability \(0.7\), what is \(P(\text{not event})\)?
11. A spinner with 4 equal sections is spun. What is the probability of landing on a section numbered 1 or 4?
12. What is the probability of flipping a coin and getting tails, then rolling a die and getting a 6?
13. A die is rolled. What is the probability of rolling a number less than or equal to 2?
14. What is the probability of rolling an even number on a fair 6-sided die?
15. A spinner is divided into 8 equal sections numbered 1 through 8. It is spun once. What is the probability of landing on a number greater than 6?
16. A fair six-sided die is rolled once. What is $P(\text{rolling }1\text{ or }2\text{ or }3)$?
17. A jar contains 12 red marbles, 8 blue marbles, and 5 green marbles. If one marble is drawn at random from the jar, what is the probability that the marble is blue?
18. If a number is randomly selected from 1 to 10, what is the probability of selecting a prime number?
19. If you flip a coin twice, what is the probability of getting two heads?
20. A fair die is rolled once. If the probability of rolling a number less than 5 is $p$, what is $P(\text{not less than 5})$ in terms of $p$?
21. Two fair coins are flipped. What is the probability of getting exactly one head?
22. A bag contains exactly 5 red marbles, 6 blue marbles, and 4 green marbles. If one marble is randomly selected from the bag, what is the probability that the marble is blue?
23. Two fair, standard 6-sided dice are rolled. Given that the sum of the two dice is exactly 8, what is the probability that at least one of the dice shows a 5?
24. A jar contains 4 red marbles, 5 green marbles, and 6 blue marbles. If two marbles are drawn at random from the jar without replacement, what is the probability that both marbles drawn are green?
25. A bag contains 6 red marbles, 5 blue marbles, and 9 green marbles. If one marble is chosen at random, what is the probability that the marble is NOT blue?
26. A movie theater recorded the snack choices of its patrons and summarized them in the table. If a patron who bought popcorn is selected at random, what is the probability the patron is a child?
27. The two-way table shows the results of a survey of 200 high school students who were asked whether they play a sport and whether they play a musical instrument. Given that a randomly selected student plays a musical instrument, what is the probability that the student also plays a sport?
28. A bag contains only red and blue chips. The ratio of red chips to blue chips is $3:5$. If there is a total of 40 chips in the bag, what is the probability that a chip drawn at random will be red?
29. In a box of 12 light bulbs, 3 are defective. What is the probability of selecting a non-defective bulb?
30. A coin is flipped three times. What is the probability of getting exactly two heads?
31. If two dice are rolled, what is the probability that the sum is 7?
32. A dice is rolled twice. What is the probability of rolling a 3 and then a 4?
33. If the probability of rain tomorrow is 0.4, what is the probability that it will not rain?
34. A standard 6-sided die is rolled. What is the probability of rolling a number greater than 4?
35. A jar contains 10 candies: 4 red, 3 blue, and 3 green. If one candy is chosen at random, what is the probability that it is not blue?
36. A coin is flipped twice. What is the probability of getting two heads?
37. A box contains 12 tickets numbered 1 through 12. One ticket is selected at random. What is $P(\text{multiple of 3 or even})$?
38. A fair die is rolled once. What is the probability of rolling a number that is neither 1 nor 6?
39. Two fair six-sided dice are rolled. What is the probability that the sum of the two dice is 7?
40. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles (10 total). One marble is selected at random. What is $P(\text{red or green})$? (Assume the events are mutually exclusive.)
41. A jar contains 2 green marbles, 3 red marbles, and 5 blue marbles. One marble is chosen at random. What is $P(\text{green or red})$? (Assume these events are mutually exclusive.)
42. A bag contains 7 yellow candies and 5 purple candies. Two candies are drawn with replacement. What is the probability that both candies drawn are purple? (Assume independence.)
43. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles (10 total). One marble is chosen at random. What is the probability of not choosing a blue marble?
44. A class has 10 students: 6 are wearing glasses and 4 are not. One student is chosen at random. What is the probability the student is not wearing glasses?
45. A fair six-sided die is rolled once. What is the probability of rolling an even number or a number greater than 4? (Assume outcomes are mutually exclusive only when appropriate.)
46. A fair six-sided die is rolled twice. What is the probability of rolling a 3 on the first roll and an even number on the second roll? (Assume independence.)
47. A set of cards is numbered 1 through 20. If one card is chosen at random, what is the probability that the number on the card is a multiple of 3?
48. A survey asked 100 students whether they play a sport and whether they play a musical instrument. The results are shown in the table below. Given that a randomly selected student plays a sport, what is the probability that the student also plays a musical instrument?
49. A game involves rolling a fair 6-sided die. If the result is a 1 or 2, the player wins $6. If the result is a 3, 4, or 5, the player loses $3. If the result is a 6, the player wins $12. What is the expected value of one roll of the die?
50. A standard die is rolled. What is the probability of rolling a number greater than 4?
51. If a coin is flipped twice, what is the probability of getting exactly one head?
52. A spinner is divided into 8 equal sections numbered 1 to 8. What is the probability of landing on an even number?
53. If two dice are rolled, what is the probability of getting a sum of 7?
54. If a die is rolled, what is the probability of rolling a 2 or a 5?
55. If two dice are rolled, what is the probability of getting doubles (same number on both dice)?
56. If a die is rolled twice, what is the probability of rolling a 4 followed by a 6?
57. Events A and B are independent. If P(A) = 0.4 and P(B) = 0.3, what is the probability that both A and B occur?
58. A coin is flipped three times. What is the probability of getting at least one tail?
59. A bag contains 10 white and 15 black balls. What is the probability of selecting a white ball?
60. A jar contains 4 red and 6 blue marbles. If two marbles are drawn without replacement, what is the probability both are red?
61. A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting tails and rolling a number greater than 4? (Assume independence.)
62. Two fair six-sided dice are rolled. What is the probability that the sum is 7?
63. A bag contains 6 red marbles, 5 blue marbles, and 9 green marbles. If one marble is chosen at random, what is the probability that the marble is NOT blue?
64. A jar contains 4 red marbles, 5 green marbles, and 6 blue marbles. If two marbles are drawn at random from the jar without replacement, what is the probability that both marbles drawn are green?
65. Two fair, standard 6-sided dice are rolled. Given that the sum of the two dice is exactly 8, what is the probability that at least one of the dice shows a 5?