Probability of valve opening when closed and closed when opened

[estado3]

Homework Statement

I am trying to find the probability that a valve will be able to undergo one cycle of demand?

Given that a particular type of remotely controlled mechanical valve can be assumed to have a probability of not opening, when closed, of 0.02 and a probability of not closing, when open, of 0.01

The valve is installed in a pipeline which is to carry a fluid with the valve initially closed. What is the probability that the valve will be able to undergo one cycle of demand? I.e it will open to allow fluid to flow when required and will then close to stop fluid flowing when required to stop it.

(BTW does anyone know any software to use with Microsoft word that can add symbols such as the exponential to your word document)

Homework Equations

probability of not opening when closed = 0.02

probability of not closing when open = 0.01

The Attempt at a Solution

I am really stuck on this I am assuming a branched diagram with all the various possibilities and for one cycle I assume closed-- branches into open and closed, which in turn branches into open and closed, and to multiply out the probabilities which gave me a wrong answer(correct ans is 0.970200)

 

[Dick]

What's the probability it opens correctly? Now what's the probability it closes correctly? Now what's the probability it does both?

 

[HallsofIvy]

You hardly need a tree for just one "open-close" cycle!

 

[estado3]

Homework Statement

I see my mistake, the second part of the question now says:
In an attempt to provide additional reliability for the valve operation, two additional valves are now placed in series with the first valve on the pipeline described in question 2. Assuming that all failure events are statistically independent of each other, how does the presence of the additional values affect the reliability of the system in being able to perform one cycle of operation, namely that fluid flow should be allowed to take place when required and then be stopped.

Homework Equations

probability of not opening when closed = 0.02

probability of not closing when open = 0.01

The Attempt at a Solution

I did use a tree with three cycles i.e closed --- open with two branches, and two branches, from that and two branches from that, my answer was a little off the mark of the correct ans 0.941191