Suppose a RADAR for aircraft detection works properly with probability 0.9 (working prop-erly means the RADAR alarms if an aircraft is present and does not alarm if an aircraft isnot present). It is observed that RADARs fail independently of each other (failing means theRADAR alarms if an aircraft is not present and does not alarm if an aircraft is present).
You want to improve the reliability of such a RADAR. You build a super-RADAR system having5 RADARs in parallel, and a logic circuit that makes the decision based on majority vote, i.e., it alarms if at least 3 radars alarm and does not alarm if at least 3 radars do not alarm.
What is the probability that your super-RADAR works properly?