I think this is more of a GQ than an IMHO.
Suppose I buy a ticket for the lottery. Why would I be wrong to assume that I have a 50% chance of winning? The result as I think of it is either I will win or I won’t. So that is just 50-50.
Thanks guys. 
Because the two outcomes are not equally probable. Depending on the format of the lottery, the odds are:
You win: One in a bazillion
You lose: (A bazillion minus one) in a bazillion.
It’s very, very, very heavily weighted on the “not winning” side of the equation.
But if I try to simplify things, there will just be two outcomes, either I win or I won’t.
There is one way to improve your chances of winning the lottery.
Buy a ticket. Let’s say there are 1,000,000 tickets sold.
After the draw it is you vs 999,999 other tickets. Your chance of winning 0.0001%
Don’t check your ticket. Wait a day or 2 and hope that no winner has come forward.
Lets say 950,000 people by now have checked their tickets. It is you vs 49,999 other tickets. Your chance of winning 0.002%
Still don’t check your ticket. Wait another day or 2 and hope that again no winner has come forward.
Lets say 999,000 people by now have checked their tickets. It is you vs 999 other tickets. Your chance of winning 0.1%
If you are lucky and no winner comes forward for weeks then you will have one of only a handful of tickets that could win.
It’s genius isn’t it?
chowching, I do understand your question. Or at least, I think I do. The problem is that you understand of the phrase “chance of winning” differently than how most people understand that phrase. So, I think the best way for us to help you, is if you would clarify what you mean by that phrase.
Specifically, can you describe a situation where the chance is something OTHER than 50%? From your perspective, I cannot imagine such a situation. For example, either the sun will rise tomorrow or it won’t, so it’s 50%. Either my boss will fire me today or he won’t, so that’s 50% too.
Hmmm… If I reach into my pocket, what is the chance that the first coin I touch will be a penny? If there are no pennies in there, then the chance is 0%. If I have only pennies, then it is 100%. All other situations (including not knowing what’s in my pocket) would be a 50% chance the way you see it, because either I’ll touch a penny first or not.
Can you suggest a situation where the odds are 1/3, or some other?
So you have a 50/50 chance of dying within the next second?
There’s a 50/50 chance of nuclear annihilation tomorrow? There’s a 50/50 chance that it will snow in Las Vegas next July? There’s a 50/50 chance that President Obama will murder and eat the hostess at the Olive Garden near my house?
No, that’s not how it works. Those are very unlikely - and probability is solely about the likelihood of an event occurring - by definition. So if something is less than likely to occur, it has by definition a probability of less than 50/50.
If all you know is that there are two possible outcomes, then all you can conclude from that is that the probabilities of those two outcomes must add up to 1. In order to say that it’s 50% for each, you have to additionally show that the two outcomes are equally likely, which you haven’t even attempted to do.
The way other people see it, you can’t count it that way, because those two outcomes aren’t equally likely to happen. Figuring out “equally likely outcomes” can be very tricky.
In the lottery case, the better way to look at it is that there are MANY outcomes. You might win. I might win. John might win. Helen might win. Barack might win. You have to count up all the contestants, realize that your number is no more special than anyone else’s, and THAT’s how to count the outcomes. There’s NOT only two possible outcomes.
Here’s another great example. Roll two dice, and the total can be anywhere from 2 to 12. That’s eleven possibilities. But it is NOT eleven different outcomes, and the odds of getting any specific total are NOT one in eleven, because there are different ways of reaching each total. There are actually 36 different outcomes. There’s only one way to reach a 2, and that’s when both dice land on the 1. But there are six different combinations which total 7, so the odds of rolling a 7 are six times the odds of rolling a 2. Try it yourself and see.
I believe there is a name for the concept of “if you don’t know anything about the system, assume all outcomes are equally likely”, unfortunately I can’t remember that name right now.
Clearly it doesn’t apply to the outcomes {“win the lottery”, “lose the lottery”}, but does apply the drawing outcomes {“0-0-0-0-0-0”, “0-0-0-0-0-1”, … , “49-49-49-49-49-48”, “49-49-49-49-49-49”}. In principle we don’t really know that the drawing outcomes all have equal probability (the ink on the balls might be arranged such the “35” has a very slightly lower chance of coming up, &c), but for the sake of modelling we apply the principle and say all drawings are equally likely.
I’ll agree that you and I don’t have personal knowledge of the equal probability, but the many lottery commissions do claim to work very hard at insuring equal weights of all the numbers and that sort of thing.
The Principle of Indifference sounds like what we’re thinking about here. And yes, I was thinking about it even before I got to your post. 
Sure, if you simplify things by leaving out the important facts, they get simpler, but also, wrong.
Thanks for the reply guys. I understand what you are saying. Not all outcomes are equally probable. That is how I see it too. But this thought in my head keeps trolling me. Yes there are many outcomes but those outcomes are independent of each other. I have a 50-50 chance. You have a 50-50 chance. John have a 50-50 chance. Everyone who bought a ticket have a 50-50 chance.
So when will outcomes be equally probable?
In the end, leaving (or including) important facts, there will still just be two possible outcomes. Either it will happen or not.
Yup, two outcomes with completely different likelihoods of occurring.
Here’s a simple exercise: Will you bet me one thousand dollars that President Obama will be struck by a meteor tomorrow? It’s 50/50, so it’s a fair bet, right?
Actually, instead of making fun of your comically poor understanding of the concept, it probably makes more sense for me to offer this link:
It might help you.
So far things fell to the 50% chance that I will not die. I will not take your bet because I perceive that since the president has not been struck by a meteor the past day, he will not be struck by a meteor tomorrow. Sort of a gambler’s fallacy. Thanks for the link though.
Actually if he were to be struck by a meteor today, I would think that would make it much less likely he would be struck by one tomorrow.
Well, your intuition is leading in you in the right direction, and that’s good.