Suppose a RADAR for aircraft detection works properly with probability 0.9. It is observed
that RADARs fail independently of each other. The aircraft is present in the air-space
with probability 0.2. You want to improve the reliability of such a RADAR. You build
a super-RADAR system having 5 RADARs in parallel, and a logic circuit that uses the
maximum posterior probability detection. What is the probability that your super-RADAR
works properly?
Since they are all in parallel, only one has to work. So I thought I should use the formula: 1-(1-0.9)^5 to solve the whole problem. This seems too easy though. Then I thought of combining the reliability of the detection with the chance of an aircraft being present, giving 0.9*0.2=0.18. Then I solve for that: 1-(1-0.18)^5 = 0.63. Next, solve for the chance of an aircraft actually being present: 1-(1-0.2)^5=0.67. Then divide the first by the second: 0.63/0.67=0.936, giving the total reliability of the array. I still think this is incorrect, however. Any tips?
that RADARs fail independently of each other. The aircraft is present in the air-space
with probability 0.2. You want to improve the reliability of such a RADAR. You build
a super-RADAR system having 5 RADARs in parallel, and a logic circuit that uses the
maximum posterior probability detection. What is the probability that your super-RADAR
works properly?
Since they are all in parallel, only one has to work. So I thought I should use the formula: 1-(1-0.9)^5 to solve the whole problem. This seems too easy though. Then I thought of combining the reliability of the detection with the chance of an aircraft being present, giving 0.9*0.2=0.18. Then I solve for that: 1-(1-0.18)^5 = 0.63. Next, solve for the chance of an aircraft actually being present: 1-(1-0.2)^5=0.67. Then divide the first by the second: 0.63/0.67=0.936, giving the total reliability of the array. I still think this is incorrect, however. Any tips?
