I know someone who taught math to low-ability kids, and reported finding it difficult to persuade them otherwise. I assume some number of them carried on into adulthood still doing it.
I feel that even an underachieving student can understand that the probability of winning the lottery is not 50⁄50. I can’t imagine that many of those kids carried that fallacious thinking into adulthood.
I suspect there has to be a degree of mental disconnect, where they can see that things don’t all happen (or not happen) equally as often as each other, but answering the math question of “What’s the probability?” feels like a more abstract and different thing.
Maybe mixed up with some reflexive learned helplessness of not really trying to do math because of past experience that’s left them thinking they just can’t get it.
Possibly over generalising from early textbook probability examples involving coins and dice, where counting up and dividing by the number of possible outcomes is a workable approach.
I agree with your point about there being a ‘mental disconnect’. It seems to be less of an issue with understanding the concept of two events not being equally likely to occur, but rather an issue with applying mathematical reasoning to an abstract problem. If you can’t find the answer to that problem, you are likely to use the seemingly plausible but incorrect reasoning that ‘it either happens or doesn’t, so it’s 50⁄50.’ This fallacy could be considered a misapplication of the principle of insufficient reason.
I know someone who taught math to low-ability kids, and reported finding it difficult to persuade them otherwise. I assume some number of them carried on into adulthood still doing it.
I feel that even an underachieving student can understand that the probability of winning the lottery is not 50⁄50. I can’t imagine that many of those kids carried that fallacious thinking into adulthood.
I suspect there has to be a degree of mental disconnect, where they can see that things don’t all happen (or not happen) equally as often as each other, but answering the math question of “What’s the probability?” feels like a more abstract and different thing.
Maybe mixed up with some reflexive learned helplessness of not really trying to do math because of past experience that’s left them thinking they just can’t get it.
Possibly over generalising from early textbook probability examples involving coins and dice, where counting up and dividing by the number of possible outcomes is a workable approach.
I agree with your point about there being a ‘mental disconnect’. It seems to be less of an issue with understanding the concept of two events not being equally likely to occur, but rather an issue with applying mathematical reasoning to an abstract problem. If you can’t find the answer to that problem, you are likely to use the seemingly plausible but incorrect reasoning that ‘it either happens or doesn’t, so it’s 50⁄50.’ This fallacy could be considered a misapplication of the principle of insufficient reason.