A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.75 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process.
What is the probability that both pieces of pipe are between 10.22 feet and 10.43 feet long? Give your answer to four decimal places. Hint: Try to avoid doing calculus to solve this problem.