Please listen to this song for inspiration during this homework.

## Exercise 1

Suppose you are a PokÃ©mon Trainer in the Kanto region. You are currently walking through the tall grass of Viridian Forest on your way to Viridian City. When walking through talk grass, you will encounter wild PokÃ©mon. PokÃ©mon encounters happen one-at-a-time and you may assume they are independent.

In Viridian Forest, there are five potential PokÃ©mon that you may encounter. The following shows the probability that any one encounter is a particular PokÃ©mon, as well as the PokÃ©monâ€™s type.

PokÃ©mon Caterpie Metapod Weedle Kakuna Pikachu
Probability 0.05 0.05 0.50 0.35 0.05
Type Bug Bug Bug, Poison Bug, Poison Electric

(a) Suppose you encounter 10 PokÃ©mon. What is the probability that at least 1 is a Pikachu?

(b) Suppose you encounter 10 PokÃ©mon. What is the probability that more than 7 are type poison?

(c) What is the probability that you see your first Pikachu after your tenth encounter?

(d) What is the probability that you see your third Pikachu on your twelfth encounter?

(e) Suppose you encounter 8 PokÃ©mon. What is the probability that it is 2 Pikachus, 4 Weedles and 2 Kakunas?

## Exercise 2

The PokÃ©mon probabilities in Exercise 1 are from the 1998 video game PokÃ©mon Red. Also released at the same time was PokÃ©mon Blue. The games are extremely similar. One difference, is the proportion of certain PokÃ©mon found in certain locations. For example, in Viridian Forest, the proportion of Metapod is: