What fraction of snowflakes are stellar dendrites?
Snowflakes fall one after another. Each flake is either a "stellar dendrite" or some other shape. The shape of each flake depends only on the previous flake: if the previous flake was a stellar dendrite, the next one is too with probability p; otherwise the next one is a stellar dendrite with probability q.
After a long snowfall you pick a flake at random from the ground.
What is the probability that it is a stellar dendrite? Express the answer in terms of p and q, and check it in the special case p = q.
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Let s be the long-run fraction of stellar dendrites. A flake is a stellar dendrite either because the previous one was and it stayed (probability p), or because the previous one was not and it switched (probability q). Write s in terms of itself.
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