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?

Show hints (2)+

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

Reveal answer →

0.7742 (± 0.001)

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise free Unlock solutions

Asked at: Jane Street, Optiver

Cats and dogs on the street

Answer

Related questions