(d) (5%) Derive E[X]. [A detailed derivation is required.]

5. (15%) Red Rose tea randomly began placing 1 of 6 English porcelain miniature figurines in a 100-bag box of the tea, selecting from 6 nautical figurines, which are numbered 1 to 6. (a) Let \( X \) denote the number of Red Rose tea that a family would have to buy to have at least three of the nautical figurine having number 1. Write down the probability mass function of \( X \).