(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 $\text{P}(X') + \text{P}(Y') = 2 - 2a + b$.