Hi, hope someone can help! In an automotive application, an emissions monitor tests a system intermittently. If the system is faulty then the 'check engine' light must be illuminated on the dashboard.
The legislation says that if the fault is detected on 2 successive occasions then the light must be lit. This is so that one rogue result doesn't light the light.
Let us say there is a fault with the system being monitored. When there is a fault, the monitor correctly diagnoses it 70% of the time. If the monitor runs, say, 10 times, what is the probability that there will have been 2 successive detections of the fault.
I can compute the probability of 2 or more detections in 10 trials using the Binomial distribution. Integrating nCx . p^x . q^(n-x) for x = 2:n, where n=10, p = 0.7; q = 1-p.
But this obviously isn't the answer because the 2 detections need to be CONSECUTIVE. So, how do I calc the probability?
It seems like it should be really simple but I'm not a mathematician and therefore not clever enough to see it!
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