Calculating Probability of Subsea Compressor System Failure

[abba02]

[SOLVED] Bolean Algebra

Question
The failure of a subsea compressor system is described by the following Boolean
Algebra statement:
F = A UBU(CUD)
If P[A] = 0.01; P = 0.0034; P[C] = 0.00067; P[D] = 0.002, calculate the probability
P[F] given independence between A,B,C,D.
ANSWER[0.013367]

ATTEMPTS AT PROBLEM
I have tried to use the associative expression to solve this but my answer is different from the given answer of .013367

 

[tiny-tim]

Welcome to PF!

Hi abba02! Welcome to PF!

(btw, this probably ought to be in the coursework and homework section)

Show us your attempt, and then we'll know how to help you.

[And are you sure it's not F = A UBU(C∩D)?]

 

[abba02]

My attempts to solve the problem

It is F = AUBU(CUD)
I had derived the below using the associative law. But after plugging in the values of A,B,C and D , my answer were still different from the given answer.
P(A) +P(B) +P(CUD)-P[A]P-P[A]P[CUD]-PP[CUD]+P[A]PP[CUD]

 

[tiny-tim]

… looks good to me …

Hi abba02!

Yes, your method looks good to me!

(though it would be quicker to say P(notF) = P(notA)P(notB)P(notCUD))

ok, now try it with f = A UBU(C∩D), and see what you get.

 

[abba02]

Thanks, With your advise, I have got the solution to the problem. I think that the problem must have been stated wrongly.