Cats and dogs on the street

MediumBrainteasers~6m

Walking down a very long street, you observe that $\tfrac67$ of the cats are immediately followed by a dog, while $\tfrac14$ of the dogs are immediately followed by a cat. In the long run, what proportion of the animals are dogs?

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Count adjacencies: cat $\to$ dog transitions number $\tfrac67 C$ ; dog $\to$ cat transitions number $\tfrac14 D$ .
In a long line these transition counts must match. Set them equal and solve for $D/(C+D)$ .

Answer

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0.7742 (± 0.001)

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Cats and dogs on the street

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