is it possible then that the answer is (0.3)^2 because the letters in the middle do not really matter? This is just me guessing but if the stuff in the middle doesn't matter then we can simply treat the whole problem as if it were a sequence of two?
Given three characters that have a specific probability assigned to each of them:
Ω: .2
θ: .3
β: .4
What is the probability of having, say a sequence of 6 of these characters where the first and last character is a θ?