University of California Berkeley Probability Density Fuctions Questions

1. The company Random Cereal places figurines in cereal boxes via thefollowing process: in each box, with probability 1/2 it places nofigurine in the box, and with probability 1/2 it places some figurine inthe box. When it places a figurine, it chooses one of 4 possible typesuniformly and random.

(a) Suppose you have collected k of the 4types of figurines, where k E (0,1,2,3) (collecting a type of figurinemeans that you have at least one figurine of that type). What is theexpected number of cereal boxes you need to open until you obtain a newtype of figurine (that you have not already collected)? Your answershould be in terms of k.
(b) Suppose you do not have any of the figurines. What is the expected number of boxes you need to
open to collect all 4 types of figurines?