Pattern on Snowflakes

Snow-particles are falling on the ground one after another. A particular snowflake turns out to be of type "Stellar Dendrite" with probability '$p$' if its previous particle was also Stellar Dendrite, and with probability '$q$' if previous one was something else. If a snowflake is picked from ground, what is the probability that it is Stellar Dendrite? Calculate for $p=1/2$ and $q=1/3$
PS:Although no two snowflakes are alike, yet there are various crystalline structures to categorize their interesting shapes. The most popular shape, called Stellar Dendrites means star-like particles with tree-like branches.