Question 1: A class has 30 students. 18 like basketball, 12 like soccer, and 8 like both. Calculate the probability that a randomly selected student likes either basketball or soccer.

Answer: 0.8

Question 2: In a survey, 50% of people own a car, 30% own a bicycle, and 20% own both. What is the probability that a randomly chosen person owns neither a car nor a bicycle?

Answer: 0.2

Question 3: Construct a Venn diagram representing the following data: Out of 100 students, 60 like chocolate, 40 like vanilla, and 25 like both. Use the diagram to find the probability that a student likes only vanilla.

Answer: 0.15

Question 4: If the probability that it rains on any given day is 0.3, and the probability that it is cloudy is 0.5, with a 0.2 chance that both happen, what is the probability that on a randomly selected day, it is either rainy or cloudy?

Answer: 0.6

Question 5: A survey shows 70% of students prefer tea, 50% prefer coffee, and 20% prefer both. What is the probability that a student prefers neither tea nor coffee?

Answer: 0.2

Question 6: A manufacturing plant produces 5% defective items. If 10 items are selected at random, what is the probability that exactly 2 are defective? (Use binomial probability formula)

Answer: 0.158

Question 7: A box contains 20 red balls and 30 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?

Answer: 0.095

Question 8: In a class, 40 students like math, 25 like science, and 10 like both. If a student is chosen at random, find the probability that they like only math.

Answer: 0.3

Question 9: A survey shows 80% of people like ice cream, and 65% like cake. If 50% like both, what is the probability that a person likes either ice cream or cake?

Answer: 0.95

Question 10: A company has 3 machines. Machine A produces 50% of the items, Machine B produces 30%, and Machine C produces 20%. The defect rate for Machine A is 2%, for Machine B 3%, and for Machine C 1%. What is the overall probability that an item selected at random is defective?

Answer: 0.023

Question 11: A student randomly picks a card from a deck. The card could be a red card or a face card. What is the probability that the card is red or a face card?

Answer: 0.49

Question 12: Error Analysis: A student calculates the probability of two events both happening as 0.4, but forgets to account for overlap and gets 0.6. Identify the mistake and correct the probability assuming the events are independent.

Answer: The student forgot to subtract the intersection. Correct probability = 0.4 * 0.4 = 0.16.