Question 1: If the probability of event A is 0.3 and event B is 0.4, and they are mutually exclusive, find P(A or B).

Answer: 0.7

Question 2: Calculate P(A or B) when P(A) = 0.2, P(B) = 0.5, and events are mutually exclusive.

Answer: 0.7

Question 3: If P(A) = 0.6 and P(B) = 0.3, are events A and B mutually exclusive? Explain your reasoning.

Answer: No, because P(A or B) ≠ P(A) + P(B); they could overlap.

Question 4: A bag contains 5 red and 3 blue balls. Probability of drawing a red ball is 0.625. If a second ball is drawn after replacing the first, find the probability both are red, assuming events are mutually exclusive in successive draws.

Answer: 0.390625

Question 1: Two events, A and B, are mutually exclusive. P(A) = 0.4, P(B) = 0.3. What is P(A or B)? Justify your answer.

Answer: 0.7 because P(A or B) = P(A) + P(B) for mutually exclusive events.

Question 2: A die is rolled. Event A: landing on an even number. Event B: landing on a number greater than 4. Are A and B mutually exclusive? Calculate P(A or B) if they are mutually exclusive.

Answer: P(A)=0.3, P(B)=0.2, so P(A or B)=0.5

Question 3: Explain why the formula P(A or B) = P(A) + P(B) does not hold if events A and B are not mutually exclusive. Illustrate with an example.

Answer: Because P(A and B) ≠ 0, so need to subtract P(A and B) to avoid double counting.

Question 4: In a class of 30 students, 10 study Math, 8 study Science, and 3 study both. Find the probability that a student studies Math or Science. Are the events mutually exclusive?

Answer: P(M)=10/30=1/3, P(S)=8/30=4/15, P(M∩S)=3/30=1/10; P(M or S)=1/3+4/15−1/10=7/15; Not mutually exclusive.

Question 1: A survey shows 20% of people prefer tea and 15% prefer coffee. If 5% prefer both, find the probability that a person prefers either tea or coffee.

Answer: 0.3

Question 2: In a factory, 10% of products are defective. If the defects are independent, what is the probability a product is defective or non-defective? Determine if the events are mutually exclusive.

Answer: P(defective)=0.1, P(non-defective)=0.9; P(defective or non-defective)=1; Not mutually exclusive.

Question 1: Two events A and B are mutually exclusive with P(A)=0.25 and P(B)=0.35. Find P(A or B) and explain why the formula applies.

Answer: 0.6, because P(A or B) = P(A)+P(B) for mutually exclusive events.

Question 2: A spinner is divided into 4 equal sectors numbered 1 to 4. Event A: landing on an even number. Event B: landing on a number greater than 2. Are A and B mutually exclusive? Calculate P(A or B).

Answer: P(A)=0.5, P(B)=0.5, P(A∩B)=0, so P(A or B)=1.0

Question 1: A student calculates P(A or B) as P(A) × P(B) for mutually exclusive events. Is this correct? Explain and correct if necessary.

Answer: No, because P(A or B) = P(A)+P(B); multiplication applies for independent events, not mutually exclusive.

Question 2: A student forgets to subtract P(A and B) when calculating P(A or B) for non-mutually exclusive events. Provide an example problem and show the correct calculation.

Answer: For P(A)=0.5, P(B)=0.4, P(A and B)=0.2, correct P(A or B)=0.5+0.4−0.2=0.7