N2019 P2 Q8

Gerri collects characters given away in packets of breakfast cereal. There are four different characters: Horse, Rider, Dog and Bird. Each character is made in four different colours: Orange, Yellow, Green and White. Gerri has collected \(56\) items; the numbers of each character and colour are shown in the table.

1. Gerri puts all the items in a bag and chooses one item at random.
   1. Find the probability that this item is either a Horse or a Rider.[1]
   2. Find the probability that this item is either a Dog or a Bird but the item is not White.[1]
2. Gerri now puts the item back in the bag and chooses two items at random.
   1. Find the probability that both of the items are Horses, but neither of the items is Orange.[1]
   2. Find the probability that Gerri’s two items include exactly one Dog and exactly one item that is Yellow.[3]
3. Gerri has two favourites among the \(16\) possible colour/character combinations. The probability of choosing these two at random from the \(56\) items is \(\frac{1}{77}.\) Write down all the possibilities for Gerri’s two favourite colour/character combinations.[3]