I did count correctly, there were 52 blue balls selected, either first or second.
There were 51 out of 51 blue balls selected first. I seriously doubt that out of 51 blue and 49 red that EXACTLY 51 blue balls were selected first.
How many times was this experiment run until getting the desired outcome???
That is where you are mistaken.
If you chose the right bag - you know the next ball. There was 98% chance of getting the right bag - so 98% chance that the next ball is blue.
You are ignoring that you only get to pick out of the bag you already chose. You do not have a choice of 99 more balls - only 49 balls. And you know that you had 98% that those 49 are all blue.
You don’t understand the point of this exercise right now.
I didn’t run any experiment. It’s made up data. I asked you to construct a dataset – that means “make it up”. Literally, just make up some results.
I’m not asking you to run an experiment, I’m asking you to literally just make up some results.
If you’re capable of making up some results that have the statistics that you think should be there, I’m going to send you $100. You don’t have to run any experiments, you just have to make up some data that’s consistent with your statistics.
That’s all you have to do. If you can make it up, you win $100.
You also did not count correctly, still, but that’s beside the point. Make up some data that has your statistics, that’s the real point here.
That’s your mistake. There was a 50-50 chance of selecting either bag. There was a 98% chance that after selecting a blue ball that it came from the bag with 50 blue balls.
That is the point. The question is about the chances AFTER you already selected one blue ball - it isn’t about “from the beginning in complete ignorance”. It is about reassessing your chances ONCE YOU KNOW that you selected a blue ball from the bag (regardless of how you got the bag).
If you think I counted wrong then highlight the mistake in red!
There are 102 blue balls selected in the dataset.
Again, this is entirely beside the point. I’m trying to send you $100 here. All you have to do is invent a dataset that is consistent with your statistics.
The challenge is open to anyone: first person to be able to invent a dataset consistent with Motor’s expected statistics gets $100. You better act quick now, Motor, before someone else claims it first.
I’m fully serious by the way, I prepared myself mentally to part with $100 earlier today, before I said it. I can afford it, but I won’t like it.
But if someone is capable of proving the impossible, they deserve it.
No bet – he keeps changing what he is talking about - “plausible deniability”.
The dataset I’m asking to be constructed isn’t changing though, I’ve laid it out in plain detail, and it still stands the same now as it did then.
I already said there was a 98% chance that the blue ball came from the all blue bag. That does not equate to removing the chances of 1 of the other 49 red balls being selected next.
Since there are 49 red balls and 50 blue balls remaining the probability is still 49 out of 99 that you select a red ball next, just like if you started the experiment from scratch.
Knowing the chances are 98% that the bag contains all blue does not eliminate the 49 red balls from the equation.
You are basing your 98% on which bag, not the balls.
But you stated an obvious contradiction - he will have no choice but to deny that he meant what you said.
What it does is tell you that having those 49 reds is only a 2% chance. There is nothing left to it.
No. There is no math of 49 equating to 2%. There is 50 out of 51 blue balls equating to 98%. That does not equate to 49 being 2%.
Motor, I guess you don’t have any competition… for now. I still recommend you come up with the dataset sooner rather than later if you want a free $100
Asking if the next ball is blue is merely asking which bag you probably chose.
Show me how you get 2% from 49 red balls and 50 blue balls?
The calculation of which bag the blue ball came from does not calculate the 49 red balls.
Motor, I’ve been waiting all evening for a data set that shows that your statistics can be consistent with each other. It doesn’t have to be exact, I’ll give you ± 5% wiggle room either way, on both the 98% and the 49.5% number. So you have a lot of room for error.
I really want to give you this money, please try. Let me know the results of you trying to construct this data set with those properties.
Regardless of which math you personally used to get 98% probability of having the all blue bag - you have agreed to that stat.
If you chose a blue ball - which you have already done –
If you had no idea of what was in either bag - you would have to bet on merely the number of balls total (which is what you have been doing).
But you DO know that there is a 98% chance that you have the blue bag - which then gives you 100% chance the next ball is blue (because you are not selecting from 99 balls - only the 49 in that chosen bag - 98% that they are ALL blue).
He doesn’t know how to do that – and I think your example could use some improvement. 
How could my example use some improvement?