Taken from ‘The black swan’ (NNT)
You’re playing head or tail with an unbiased coin, against someone. You always choose H, he always chooses T.
You lose the first 99 draws. What is the probability that you win the 100th?
50%…?
~Matt
Waiting for a bunch of answers to have a ‘representative sample’ of the LR 
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I agree with 50%.
I was never good with stats so I’m probably wrong anyway.
~Matt
Can I change my answer? I think 0%, because no one is that lucky so that means he’s cheating and you’re gonna loose again 
~Matt
50/50
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im going to say this wrong…but here goes…
the odds of any 1 flip of that coin, including the 100th to be H is 50%.
However, the odds that you flip that coin 100 times and it coming up T all 100 times is astronomical.(too lazy to figure it out, something like .5^100)
The coin has no memory of what happened before it, or what will happen after it. In each individual flip, it is 50/50, not accounting for a small % that it might just land on it’s side and balance there. Now as to the odds of 100 of 100 being the same in a row, that will take some tinkering here, but you did not ask for that… As someone already said, it is a very big #…
Actually MJuric gave the right answer…from a purely theoretical standpoint, you could indeed say, it’s 1/2, because the coin has no memory as you point out.
However, as stated by ohiost, the odds that the first 99 draws give the same result are incredibly small…so small that from a practical standpoint, the likelihood is 0…
So, the odds that you win #100 is 0…And as a matter of fact, if you played that game against someone, you’d assume he cheats way before reaching 99…at the odds of losing the first 10 are ~ 0.0009 (1/2^10).
Funnily, when I gave that exercise in class, in a class setting, no one had any common sense
The Law of Independent Trials…or some other high fallutin’ term. It’s why Vegas saw it’s roulette take increase substantially after they put those boards up that showed the results of prior spins…
Funnily, when I gave that exercise in class, in a class setting, no one had any common sense
Common sense goes out the window when you get more involved in the problem. It’s very easy to get so involved in the complexities of the issue that you completely miss the simple answer. Of course that’s why I think in many cases I don’t trust the “Experts”. They have a tendency to over analyse and miss the easy answer.
I can easily see myself taking a math class spending hours doing problems and then going right to the “Hard calculation” and miss the easy answer. Hell I do it a lot here when designing something.
~Matt
Since you only asked the question about the 100th flip by itself, there is only one right answer…All your gobbly goop before that was just to throw off the masses. From most of the responses, you did not fool anyone here. I guess we are a lot smarter than your students…Does that say something about todays youth, or their teacher??? (-;
The funny thing is your argument ‘you only asked about the 100th flip itself’ means you didn’t understand your own answer…
truth is, we don’t really know for sure how the coin toss will turn out, yes, we can state it as a 50/50 proposition, but statistics deal with populations and we have one individual coin who gives a damn about populations (multiple coin tosses)
and it bothers us that this coin or the universe in general appears so unbothered by the lack of fairness
so we imagine a God who gets this nagging feeling that something is not right in the universe - yes indeed, an unbiased coin toss has yielded 99 heads in a row - so God is going to get up out of his/her easy chair and ‘fix’ this troublesome coin
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Ah yes, I love probability and statistics. Here’s another one.
Suppose you were to flip a coin 100 times. What is the probability that you will get 50 Heads and 50 Tails?
50 Heads and 50 Tails is the single most likely outcome you would receive, however, it is far more likely that you will get something other than that outcome.
100!/2.50! . (1/2)^100
“So, the odds that you win #100 is 0…And as a matter of fact, if you played that game against someone, you’d assume he cheats way before reaching 99…at the odds of losing the first 10 are ~ 0.0009 (1/2^10).”
Strictly speaking, one should ask the person posing such a problem whether or not the possibility of cheating is intended to be excluded before giving an answer. (If you’re not allowed to ask someone asking an ambiguous question for clarification, then the question is really unanswerable.)
If the possibility of cheating is supposed to be excluded, then the correct answer, of course, is 50%.
In some ways, the problem is reminiscent of the Unexpected Hanging Paradox. When posed with that problem, one should (in similar fashion) immediately ask whether the judge is supposed to be presumed always to be 100% honest. If he/she is, then I believe this paradox can only be resolved through a sound theory of epistemology.
50% - the previous draws have no impact on the probability of the next.
Had you asked for the probability of losing 99 and then winning the final, that would be quite different.
Did you ever see/read Rosencrantz & Guildenstern are Dead?
That’s the part where it’s important to be practical and drop theory…
The odds to have 99 draws that are identical with an unbiased coin are:
1.57772181 × 10^-30
In short, from a purely practical standpoint, it’s equal to 0. It will just not happen.