1. Two friends A and B go on a date and agree to meet at 7pm. Friend A is an impatient person and will scold b if A arrives before B and B arrives later than 7.15pm. Let X denote the number of minutes after 7pm that A arrives and Y denote the number of minutes after 7pm that B arrives. Assume that X and Y are independent and that they are both uniformly distributed on the interval (-30, 30).
(a) Draw a graph with X and Y as the two axes and shade the region which represents the event that B will be scolded.
(b) Hence, or otherwise, find the probability that B will be scolded.