A merchant has found that the number of items of two brands A and B that she can sell in a day are independent Poisson random variables with means 4 and 10 respectively. [a] What is the probability that no item of brand A will be sold in a day? What is the probability that no item of either brand will be sold in a day? (6 marks] [b] If the merchant has 8 items of brand A and 6 items of brand B in stock, what are the probabilities that she will sell out her stock of each brand individually and of both brands together in one day? (6 marks] [c] What is the probability distribution and the expected number of days out of 25 that the merchant will sell no items of brand A? (6 marks] [d] What is the probability of selling out all the stock in [b] in two days? (7 marks]