However, if her friend Irene, who is a shopaholic, goes with her, then she tends to buy more items, so that the number of purchased items still has a Poisson distribution but with a new rate ????2 = 4.5. Lucy is going to the shops next Saturday and she has invited Irene to come with her, but she is not sure if she will be coming. If the probability that Irene accompanies Lucy to the shops is 0.7, find

(i) the probability that Lucy buys at least five items;

(ii) the expected number of items she will buy.