Aking tried his political prisoners based on frank stockton’s story “the lady or the dragon’. the prisoner must choose one of two doors. behind each door is a room containing either a lady or a dragon. it is possible that both rooms contain ladies or that both rooms contain dragons, or that one room contains a lady and the other room contains a dragon. if the prisoner chooses the room with the lady, he goes free. if he chooses the room with the dragon, he is eaten. there is a sign on each door. the king tells the prisoner that the signs on the door are either both true or both false. the sign on door #1 says “at least one of these rooms contains a lady”. the sign on door #2 says “a dragon is in the other room.” which room should the prisoner pick?

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)