[SOLVED] Bolean Algebra

[abba02]

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[B] = 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]

Hi abba02! Welcome to PF! :smile:

(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. :smile:

[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[B]-P[A]P[CUD]-P[B]P[CUD]+P[A]P[B]P[CUD]

[tiny-tim]

Hi abba02! :smile:

Yes, your method looks good to me! :smile:

(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.