Hot work (torch-cutting, welding, soldering, etc.) is one of the leading causes of industrial res. The probability of a re event occurring in year in a warehouse {where hot work is prevalent) is estimated to be [115. For safety, a very sensitive re alarm system is installed. Whenever there really is a re, this system will always sound the alarm, i.e. with a probability of 100%; however, because of its high sensitivity, the system also gives false alarms, with a probability of 0.25. Assume that there can be at most one re at this warehouse in a year. (a) 'Nhat is the probability that the alarm will be sounded in a year? [3.5 pts.] (b) 1What is the probability of there really being a re, given that the alarm sounded? [2.5 pts.]