I want to find the probability that X_i=1 and X_(i+1) = 2 for 500 (independent) rolls of an unfair 6-sided die with probabilities (.1, .3, 1, .2, .1, .2). I think it's just .1 * .3 but I'm not sure whether the answer depends on i (like if you just rolled the 500th roll or something like that) or on the number of rolls (like if we did 300 rolls instead of 500)? Can someone clarify this?