# Probability mass function

1. Oct 1, 2008

### kingwinner

1. The problem statement, all variables and given/known data
Consider a system of water flowing through valves from A to B as shown in the diagram. Valves 1, 2, and 3 operate independently, and each correctly opens on signal with probability 0.8. Find the probability distribution / probability mass function for Y, the number of open paths from A to B after the signal is given (Note that Y can take on the values 0, 1, and 2.)

2. Relevant equations
Probability mass function just means finding the probabilities of all possible outcomes

3. The attempt at a solution
I don't understand the question itself so I can't get anywhere (coloured in red). Does anyone actually understand what is going on in this scenario? I would truly appreciate if somebody can explain it to me.

2. Oct 1, 2008

Start thinking this way:

when water comes in from A, it can go up or down to the different pumps.
If it goes to pump 1 there is some probability the pump operates correctly. If it goes to the bottom of the system, it pump 2 alone can operate, pump 3 alone, or both pump 2 and 3 can operate. Break things down by cases, and remember the simple multiplication and addition rules for probability. You may have to be creative in their use.
Why no more detail from this response? You need to show a little work first.
On the good news side, this type of problem is picky, and you need to watch details, but it isn't super complicated.

3. Oct 1, 2008

### kingwinner

Thanks, but do you have any idea what is going on with the "signal" that the problem talks about twice?

And what is the probability that it goes to the bottom of the system? to the top of the system? Both 0.5?

4. Oct 1, 2008

Since there is no information about the signal (no probability information, or indicated source) I take that to mean this: each gate has an $$80\%$$ of opening when it should (so a $$20\%$$ chance of failing to open to water flow).
And yes, I would also assume (you may want to ask a professor about this, just to be sure) that when water comes in from $$A$$, there is a $$50-50$$ chance that it flows up and down (or, equivalently, 1/2 of it flows up, 1/2 flows down).