A fair walk between 0 and 8

Topic: Random walks and first passage · more questions on this topic
A biased walk on four steps ›

A fair walk is absorbed at 0 and at 8, and starts at 5. Find the probability of reaching 8 before 0, and the expected absorption time.

Fair steps give hitting probability h_x=x/d and expected duration e_x=x(d-x). Here d=8 and x=5, so the probability of reaching 8 before 0 is 5/8, and the expected number of steps is 5(8-5)=15.