The USA Steel Co. uses coke and iron to produce steel in closed furnaces. Reduction of the iron and oxidation of the coke produces various gases (including CO) which are vented through flues to the atmosphere. On January 2th (the first day after the Christmas shutdown), a worker was overcome with CO in the furnace area and died. A safety inspector later pieced together the following facts: i) The facilities were antiquated, the flues contained many small cracks, ii) In a cost cutting measure over the Christmas holidays, the company had shut down all ventilation in the plant, iii) Several of the CO monitors were found to have dead batteries, iv) Contrary to company policy, the worker as not wearing an appropriate respirator. Analyze the above scenario and develop a fault tree. Assume that probability of not wearing the proper respirator is 0.1, and the probabilities of the batteries dying, the ventilators being shut off and the flue leaking are all 0.01. Calculate the probability of the head event.