Thread: 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'?

Thanks

Well... Suppose you were told that if the first application is successful, the reliability of the second application is zero. How would that change your answer?

Well I wouldn't change my answer, because the probability of failure is not really linked to the probability of success of the second coat given the sucess of the first? Inother words may be the information given at the end of the question is not relavent and the correct answer is 1-0.03= 0.97?

Right.

If the first coat succeeds, the success or failure of the second coat is irrelevant.

It was the additional info at the end of the question that threw me!! Thanks very much for your help.