What are some common misconceptions when it comes to probability

>>8449938
If it's just high-school, then a great one is that one problem with the three doors and goats.

They fail to account for the fact that "He will always choose a door with a goat behind it" is valid and relevant information, completely changing the odds of your decisions.

>>8449945
Yep just high school seniors. I teach students that don't really have a strong interest in the subject, just want a credit in their senior year. The class is mostly ACT Prep and just general life skills math.

We will be looking at the monty hall problem though. That's a good one :)

That everything has probability of 1/2 cuz it either happens or not

>>8449938

An extremely common misconception is what random distributions look like. People seem to think that streaks are somehow impossible, even though they become increasingly probable as the number of trials increases. For example, people think this would be a fair, random coin HTHHTHTTHTHHTHTHHTHTHTT but this isn't TTHTHTTTTHHTHHTTHHHTHHT because it has a streak of 4 and 3, even though those are not too improbable.

You can google a lot more about this as well.

>>8449979
Oh right!
Not OP here. I remember a story of a professor flipping a coin, and having a student make up a fake coin flip series. Then they made bets on which one was real. Everyone assumed the real flip was the fake one because it had a streak of something like five tails in a row.

>>8449984
>>8449979
It's very likely for a large amount of truly random data to have seemingly strong patterns. I think I recall an article about a method for detecting fabricated results based on insufficient clustering, and how a young researcher exposed a respected late-career colleague's misconduct with it.
Well-told interpersonal dramas are among the best ways to teach "life skills math." They attractively and succinctly answer "what is this good for?" and "when will anyone need this?"

>>8449951
Another one is Bertrand's box

For high school? Probably just the idea that independent events can affect each other.

E.g. "it's been black 5 times in a row, bet red!"

Though I don't know, on a survey people probably would be more likely to answer correctly as to their odds than if you asked them directly, because you have to explicitly name the alternative answers or even specify that the events are independent.

>>8450029
Yeah I worry students will do better on a survey than in a real situation. Any strategies to avoid this.

And appreciate all the replies. THe community on sci is awesome. No troll

>>8450010
I will have to see if I can find that specific case. Ive heard of the fake coin data set lesson before. Sounds like a really fun lesson. Excited to do that

>>8449938
There's so many news stories along the lines of "Doctors said I only had X months to live, but I'm still alive thanks to kale, prayer, homeopathy, etc", but doctors do not give diagnosis like that in the first place.

What happens is a doctor says "The mean life expectancy for someone with your illness is eighteen months", and the patient thinks that means "you have eighteen months to live".

>>8450844
You are right. I try to really emphasize that the average tells you nothing about the individual.

>>8449938
This is a great idea and I wish I could have taken a class like this in high school.

One simple idea that many people struggle to truly appreciate is that past performance does not guarantee future results. If I just flipped ten heads in a row, does that change the probability I get heads this time? Obviously not. Now what about if you're trying to choose between two stocks, one of which has consistently risen, and the other hasn't? For some reason, we're much more likely to ascribe this to the wisdom of the CEO than to random chance. Basically, thinking statistically is an admission of ignorance, and often this is a far more prudent and intellectually honest way to make decisions than trying to concoct appealing just-so stories.

Benford's law is awesome, but no good explanation for high-schoolers.

>>8452085
I googled it and this was the first hit:

>the principle that in any large, randomly produced set of natural numbers, such as tables of logarithms or corporate sales statistics, around 30 percent will begin with the digit 1, 18 percent with 2, and so on,
>and so on

lol

>>8452085
Yeah that would most likely be above some of their heads. I probably get some of the least motivated students in our building. It's the lowest track math class we offer. Not trying to downplay my kids or anything, they just lack motivation and don't really place a whole lot of value on education.

I'm going to try to make some sort of pre-test and then maybe design a week or so of lessons maybe to address some of their biggest misconceptions. I will probably post back here to look for some suggestions/ideas.