The Pokémon probabilities in Exercise 1 are from the 1998 video game Pokémon Red

Question

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

• Pokémon Red: 0.05

• Pokémon Blue: 0.35

Suppose it is 1998 and you are 12 years old. Assume Pokémon Red and Blue were both played equally. Your friend at school tells you they encountered 15 Pokémon in Viridian Forest, 3 of which were Metapod. What is the probability that your friend was playing Pokémon Red?

• Hint: What is the probability of seeing 3 Metapod out of 15 encounters in Pokémon Red?

• Hint: “Flip the conditional.”

Explanation / Answer

probability of playing any of the game out of these two is

Pr( Pokeman Red) = Pr(Pokeman Blue) = 0.5

Friend told that hefound 3 metapod out of 15 pokemon that makes the probability of Metapod in viridian forsest = 3/15 = 0.2

So, if Friend is playing Pokeom Red, the probability to find 3 out of 15 pokemon = 15C3 (0.05)3(0.95)12 = 0.031

if Friend is playing Pokeom BLue, the probability to find 3 out of 15 pokemon = 15C3 (0.35)3(0.65)12 = 0.111

So, Probability of 3 metapod out of 15 encounters = 0.031/ (0.031 + 0.111) = 0.2183

so the probability that 21.83% , friend was playing Pokemon Red.

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