S.O.S. Mathematics CyberBoard

Suppose you have a box containing one copy each of the numbers 1, 2, 3, and 4. Reach in and draw out a number. If it is even, divide it by 2 and put the result into the box. If it is odd, add 1 and put the result back in the box. Repeat this process, then draw out a third number.
1. Let X be the third number you drew out. Find the probability mass function and the probability generating function for X.
2. What is the probability that the third number you draw out is a 3, given that the second number was a 2?
3. What is the probability that the second number you drew out was a 2, given that the third is a 3?

What have you tried? Can you at least setup the problem?

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I really don't know where to start... anything to help with starting will be greatly appreciated. Can you use a Venn Diagram?

Also, please do not flood the board. We can understand if you're frustrated with the material and have a lot of questions, but if you cannot even setup a problem, then you should first be talking to your teacher. We exist to give help on specific problems where students get stuck or have a specific question, not to do tons of problems for them.

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I'm not trying to flood your board.... I simply need help. I'm sorry for trying to find more resources for my concerns. I'm not a young fresh out of high school student in college. I have been out of school awhile. I need help and I have been going to office hours, but with so many students and limited time it's hard to get lead ways on the difficult problems. I am not looking for someone to do all the work for me. I need help setting up the problem and hints on how to solve. I want to learn, not cheat. I have never been on a forum before so I didn't know how to approach it... my bad!!!

Perfect, and we're very happy to help you, it's just my job as a moderator to inform you of board conventions.

As a helpful tip: if the part you're having trouble with is setting things up, try and say so in the problem. Llikewise, if you're stuck somewhere else in the problem, show us your setup and work up to that point and where you are stuck, and we can more efficiently help you to understand to the best of our mutual abilities. Welcome to S.O.S. Math.

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I am stuck at the beginning of the problem.... this is what I have so far...
I know that the Probability Mass Function's range of variables is {1,2,3,4} and the Probability [even]=2/4 and the Probability [odd]=2/4...
I know that in order to have the PMF, I need to find:
P[x=1] =
P[x=2] =
P[x=3] =
P[x=4] =
with x being the third number drawn out....

I also know that the Probability Generating Function need to look like this:
Gx(z) = z + z^2 + z^3 + z^4 with z^k being P[x=k]

My problem is figuring out the introduction of the problem. It is confusing me completely... Is there a way to make a Venn Diagram for this to make it easier to look at??? Please help... I have been staring at it and trying numerous things that are not making any sense because the probability of each section of branches are not adding up to one.