While social distancing, people are still meeting up online (e. g. via Zoom or Skype). Suppose that friends X and Y agree to meet online, by joining the same virtual chat room sometime between 3.00pm and 4.00pm of a given day. Assume that X logs in to the chat room at a time uniformly distributed between 3.15pm and 3.45pm, while Y logs in to the chat room at a time uniformly distributed between 3.00pm and 4.00pm. 1. What is the probability that the friend that logs in first will wait less than 5 minutes for the other friend to join? 2. What is the probability that X arrives first?