All possible? Equally? Then how does only one outcome happen? By what force? What instruction? What reason?
Now you're saying that a 'random' choice has a cause?
I'm not going to play your word twisting game. So I shall repeate just in case you didn't understand before.
There are choices you can make. You have the ability to choose. Unless you are advocating zero free will then you must admit that there are several possibilities. A very solid example is you right now. You can choose to throw your computer out the nearest window. Or you can walk naked outside. Or you can simply respond. There are an infinite number of possibilities that you can choose to do. Which one you ultimately do is considered random.
I choose this example to expose your misunderstanding of causality. Causality is simple and hopefully you already have knowledge of it. But more or less in this purpose it means that you will follow along a set of choices and you "choose" based on past events. This is a form of causality.
However the possibility exists that you choose to divert from this path and do something crazy. Now the possibilities are not equal in this light. It is far more likely that you won't throw out your computer or walk outside naked.
But what about specific wording? What are the chances of you using any specific sentence? Those are more equal.
onward to the coinflip analogy. What are the chances of it having heads or tails? Do you know what the true test is? Its not the coin itself but your choices at the time. How hard you flip it, timing ect. Without pre-determination there will always be randomness.