Reliability of 2 coats of paint
Hi guys. This might seem simple but cant get my head around it.
A paint coating is applied twice at a particular location. The reliability of a coating is 0.85. Assuming the coatings are statistically dependant so that if the first fails, the probability that the second will also fail is 0.2. However if the first application is successful, the reliability of the second application is unchanged at 0.85. What is the probability of at least one coating being successful?
Assuming A and B are the failure events
P(A)=0.15 and P(B/A) =0.2
P(A)xP(B/A)= 0.03 is the probability failure of both layers
But how do we deal with the second part of the question ie. if 'the first application is successful, the reliability of the second application is unchanged at 0.85'?