• Welcome! The new FreeMathHelp.com forum is live. We've moved from VB4 to Xenforo 2.1 as our underlying software. Hopefully you find the upgrade to be a positive change. Please feel free to reach out as issues arise -- things will be a little different, and minor issues will no doubt crop up.

Reliability Probability


New member
Jan 24, 2011
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?


Staff member
Apr 12, 2005
I think the aircraft has nothing to do with proper operation of the array. The question, as stated, is "works properly". You don't want it to sound an alarm when nothing is there, do you? Let's not complicate it. Go with your first impression.