(a) Out of two bags, bag I contains 3 red and 4 white balls and bag II contains 8 red and 6 white balls. A die is thrown. If it shows a number less than 3 then a ball is drawn at random from bag I, otherwise a ball is drawn at random from bag II. Find the probability that the ball drawn from one of the bags is a red ball. OR (b) The probability of simultaneous occurrence of atleast one of the two events X and Y is a. If the probability that exactly one of the events X, Y occurs is b, prove that $\text{P}(X') + \text{P}(Y') = 2 - 2a + b$.

Year	Paper Code	Set	Position
CBSE 2026	Series 65-1	Set 1	Question 31
CBSE 2026	Series 65-1	Set 2	Question 29
CBSE 2026	Series 65-1	Set 3	Question 27

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)