Your alarm system has a main alarm and a backup alarm. This tree diagram illustrates all the possible outcomes of the failure or non-failure of first the alarm and then its backup. Note that it is possible for both alarms to go off and for both alarms to fail; they are independent of each other. Using this tree diagram, compute the probability of system failure. Follow each branch to find all possible favorable outcomes for success, and then use that value to find the probability of system failure.