One thing has already been proven:
The maths dummies are 100% likely to come up with more excuses not to learn.
No its not. Itâs just not. What would be better would depend what the the variables are.
Using Baysian methods, given absolutely no prior knowledge about the weather, one might reasonably choose 50% as the likelihood of rain the next day for an initial estimate. One might temper that with common sense if there is further information, for example you look out a window and see an endless expanse of sand or a rain forest, or if you have a collection of old weather reports.
As you pass each day and attend to the weather and accumulate more data your estimate of the probability of rain the next day increases in accuracy and confidence. You might even find that your estimated probability varies with the passing of seasons.
For the roll of a die or your chances of winning a lottery, there are common sense factors such as counting the number of sides of the die or estimating how many raffle tickets were sold.
One of my favorite Bayesian statistics examples (and the difference from classical statistics) is flipping a coin. If I flip a coin 100 times and it comes up heads 100 times, what is the probability of it coming up heads on the next toss?
Classical statistics say that the previous flips are independent and the probability is 50%.
Bayesian statistics say itâs 100%, as itâs more likely youâre using a two headed coin.
Well, yes - without the extra knowledge that âa dice typically has six sidesâ or âthe word six implies there are at least five other sidesâ, 50/50 would be a fair first attempt.
Consider âIâll toss a flaan. It can show a targ, or not. Rate the chance of getting a targâ. That is an honest example of âno extra informationâ.
As for rain, Jim Kirk nailed it. Adding observations, or known facts (âweâre in a monsoon seasonâ), will of course refine it away from 50%. But given that these were kids, probably in a temperate area of the USA, and probably not in a drought ⌠it could rain tomorrow. Or it could not. Anything beyond that would take more historical observations (or forecasts) than they were likely to have at hand.
How hard is it to understand âas a first approximationâ, or âgiven no further informationâ?
I didnât get the impression from âthe probability was 50% since it would either rain or notâ that the kids were estimating that rain/not rain were equally likely. I thought they were suggesting that generally, when there are two possible outcomes, they are equally likely. If that was the case, she should have corrected them. Maybe I misunderstood her.
I am reminded of the Monty Hall problem.
From the article:
One student had seen the weather and knew there was a 90% chance of rain the other had not seen the weather and though the probability was 50% since it would either rain or not. They compromised and picked the middle but thatâs not the part I cared about, I cared that they had a reasonable discussion about their thoughts.
The point was to get the students engaged in discussing their reasoning processes, which they did, and the student who initially thought that the probability of rain was 50% did not persist in that idea, because she was persuaded by the other student. In this case, there wasnât a need for the teacher to directly intervene, which is better, because itâs difficult to do so without overwhelming the discussion between students with the teacherâs authority.
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Being British I always feel a weird tugging sensation inside my head (maybe even my soul) when someone stops âMathsâ one letter to early. Iâm left without a sense of closure and with an âsâ shaped hole in the Universe. 
Right, I see what youâre getting at. I didnât quite get the same impression, obviously.
Unfortunately, they pooled one studentâs mistaken ideaâthat because there are two options the probability must be 50%, with the other studentâs better answer based on more information and came up with an answer that was less wrong for one and less correct for the other.
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