The lifetime of a turtle is a continuous value uniformly distributed between 50 and 150 years. Let X and Y be the lifetimes of two randomly chosen turtles, and consider the following events: A = {X < Y } B = {The average of X and Y is less than 100} C = {|X -100| < T }, where T is a fixed number between 0 and 50 (a) Show that events A and B are independent. Include a diagram of the sample space and the events to support your answer. (b) Show that events A and C are independent, regardless of the value of T.