2. Past data show that the probability of a married woman of age 32 being alive in 30 years' time is 0.69. Similarly, the probability of a married man of age 35 being alive in 30 years' time is 0.51. Calculate, for a married couple (woman aged 32, man aged 35), the probabilities that in 30 years' time: (i) they are both alive; (ii) only (exactly) one is alive; (iii) neither is alive. 3. A firm produces 55 percent of items on production line A and 45 percent on line B. In general, 3 percent of the products of line A and 5 percent of that of line B are found to be defective but, once a product is packaged and sold, it is not possible to tell by which line it was manufactured. If an item is subsequently returned as faulty, what is the probability that it was made on line A?