untold pebble
in the f) part, p represents the probability of absorption into the recurrent states without a single win and q refers to the probability of transitioning from deck 2 to deck 1. the probability of completing atleast 1 cycle(deck 1 to deck 2 and then again to deck 1 ) is 1-p. given that atleast 1 cycle is completed, the probability distribution of the number of wins is given to be (1-pq)^(k-1).pq. but in this case, doesnt the 1-pq term also include the probability in which after completing a cycle there is a transition from deck 1 to 1(loss), why is that included in winning? very confused!!!!!!
signal ravine