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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 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?

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**