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Suppose you are a PokÃ©mon Trainer in the Kanto region. You are currently walking through the tall grass of Viridian Forest. 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?

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:

- PokÃ©mon Red:
**0.05** - PokÃ©mon Blue:
**0.35**