Question: The website Noot!.com sells one aquatic thing (like newts) each day. Every so often, the item for sale is a Bag of Carp, recognizable by its iconic chartreuse question mark on a plain brown lunch bag. A Bag of Carp contains three random carp-related items from the Noot! Over stock. The possibilities are preserved and salted dried carp snacks (for people to eat), living koi, photos of carp in the wild, origami carp, crocheted carp, bead-knitted carp, aquatic insect pieces (for feeding carp), books on caring for carp, or a CD of carp music (made by carp for carp). Each item in a Bag of Carp is equally likely to be any of these possibilities.
(a) Let R be a random variable that indicates whether the Bag of Carp contains a representation of carp (R = 1) or not (R = 0). Compute E[R].
(b) Let C be a random variable that indicates whether the Bag of Carp contains an item that can be used by a pet carp (C = 1) or not (C = 0). Compute E[C].
(c) What is P(R = 1 and C = 1)? How about P(R = 1 or C = 1)?