Reconsider the first example in Sec. 5.2. Based on the ambiguous depth indication and the utilities, the engineer used a long pile even though the shallow depth was more likely. Would this still be the correct action if the instrument had indicated a shallow depth? How large would the "error probability" P[z0 | θ1 ] have to be before the long pile would be the better decision no matter what depth the test indicated? Would the test be justified at any cost in this circumstance?