doctors are interested in seeing what type of arch support helps the most to alleviate foot pain. twenty five volunteers are asked to wear one type of arch support one week and rank their level of pain on a scale from one to ten. the next week, they wear another type of arch support and once again rank their pain. the type of arch support that each participant used the first week was randomly selected from the two types. which arch support is better?

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)