An over temperature warning system has five temperature sensors. To prevent false alarms, the system is designed so that three or more of the sensors must sense over temperature before a warning signal is given. Assume that the probability of any single sensor failing is equal likely and that three sensors are in a failed state. However, as the inspector, you are not aware of the failed sensors.
If three sensors are selected at random for inspection, what is the probability that the system will be found in a failed state? Please explain equation used and steps to solve the problem.