Question 1: If the probability of rain tomorrow is 0.3 and the probability of snow tomorrow is 0.2, and these events are mutually exclusive, what is the probability that it will rain or snow? Calculate and show your work.

Answer: 0.5

Question 2: A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability it is red or blue, assuming these are mutually exclusive events? Calculate.

Answer: 1

Question 3: In a class, 60% of students prefer apples and 25% prefer oranges. If a student prefers either apples or oranges, and these preferences are mutually exclusive, what is the probability that a randomly selected student prefers apples? Show your reasoning.

Answer: 0.6

Question 1: A die is rolled. Event A is rolling a 2, and Event B is rolling a 4. Are these events mutually exclusive? If yes, what is P(A or B)? If no, explain why and calculate appropriately.

Answer: Yes, mutually exclusive; P(A or B) = 1/6 + 1/6 = 1/3

Question 2: A card is drawn from a standard deck. Event A is drawing a king, and Event B is drawing a queen. Are these events mutually exclusive? Use the formula P(A or B) and justify your answer.

Answer: Yes; P(A or B) = 4/52 + 4/52 = 8/52 = 2/13

Question 3: In a survey, 30% of people like tea, and 50% like coffee. If these preferences are mutually exclusive, what is the probability that a randomly selected person likes either tea or coffee? Show your calculation.

Answer: 0.3 + 0.5 = 0.8

Question 1: A factory produces parts, where 10% are defective and 15% are scratched. If these defects are mutually exclusive, what is the probability that a randomly selected part is either defective or scratched? Explain your reasoning.

Answer: Yes, mutually exclusive; 0.10 + 0.15 = 0.25

Question 2: A survey shows 40% of students prefer basketball, 25% prefer soccer, and these preferences are mutually exclusive. What is the probability a student prefers either basketball or soccer? Show your work.

Answer: 0.4 + 0.25 = 0.65

Question 1: A spinner has 4 colors: red, blue, green, and yellow. Event A: landing on red, Event B: landing on blue. Are these events mutually exclusive? Use the formula P(A or B). What common mistake might students make in calculating this? Explain.

Answer: Yes; mistake: adding probabilities without confirming mutual exclusivity. Correct: P(A or B) = 1/4 + 1/4 = 1/2.

Question 2: A jar contains 3 green balls, 4 yellow balls, and 2 purple balls. If you mistakenly assume green and purple are mutually exclusive, but in fact they are not, what error does this lead to in probability calculation? How should it be correctly approached?

Answer: Error: assuming events are mutually exclusive when they are not; correct: use the general addition rule P(A or B) = P(A)+P(B) - P(A and B)

Question 1: Student calculates P(A or B) as 0.4 + 0.3 = 0.7, claiming A and B are mutually exclusive. Is this correct? If not, what is the mistake?

Answer: No; mistake: A and B are not mutually exclusive, so must subtract P(A and B).

Question 2: In a survey, 20% like apples and 15% like bananas. A student adds 20% and 15% to get 35%, claiming the events are mutually exclusive. Is this correct? Explain.

Answer: No; they are not necessarily mutually exclusive, so need to check if they overlap; if not, sum is correct.