OK, man, GO!

Probability Level 4

Every day Crazy Jake wanders randomly from his countryside cottage. 2 3 \dfrac{2}{3} of the time he ends up in the desert, and 1 3 \dfrac{1}{3} of the time he ends up at the beach.

When he gets to his destination he plays an obscure little game on his phone called "OK, man, GO!". This is a game where he hunts for little cartoonish creatures.

Now, if he's at the beach, each creature he finds has an 80% chance of being a Magikarp. If he's in the desert, each creature he finds has only a 10% chance of being the Magikarp.

Got it?

So now for the question...

If he goes about on his journey one day, and when he gets there he only finds two creatures and they are both Magikarp, what is the probability he is at the beach?

Round your answer to 2 decimal places.

Image credit: hoopa-u.tumblr.com


The answer is 0.97.

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Geoff Pilling by Geoff Pilling , 53, USA

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2 solutions

Geoff Pilling
Aug 2, 2016

Consider the following notation:

  • B ---> Arrives at the beach
  • D ---> Arrives at the desert
  • 2M ---> Both monsters are Magikarp
  • P(A|B) ---> Probability of A given B

Then, by Baye's theorem:

P ( B ∣ 2 M ) = P ( 2 M ∣ B ) P ( B ) P ( 2 M ) = 0.97 P(B|2M) = \frac{P(2M|B)P(B)}{P(2M)} = \boxed{0.97}

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Brilliant's first PokemonGo question! We did it!

Pi Han Goh - 4 years, 10 months ago

Is this solution correct? We know that the probability of arriving at the dessert and getting two Magikarps is 2/3 1/10 1/100 which is 2/300 and arriving at the beach and getting two Magikarps is 1/3 8/10 8/10 which is 64/300. So knowing that we have two Magikarps we know that the probability that we are at the beach is 64/(64+2) which is 0.969 ~ 0.97

Jan Chomiak - 4 years, 10 months ago

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  • (2/3) (1/10) (1/10) (1/3) (8/10) (8/10)

Jan Chomiak - 4 years, 10 months ago

Yes... 0.97... That's the correct solution, 0.97. :^)

Geoff Pilling - 4 years, 10 months ago
Zachary Silver
Aug 10, 2016

The probability that crazy jake goes to the desert and both monsters being magikarp is (P(desert))(P(both magicarp))=(2/3)(1/100)=1/150. By that same thinking, the probability of going to the beach and catching only two magicarp is (1/3)(16/25)=16/75=32/150 So, if jake catches two magicarp, there is a 32/33, or about 97 percent chance of him being at the beach

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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