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I had a professor in college--teaching a queueing theory class no less--claim it was 1/3 as long as you didn't care about the order, and I interrupted the class

I had a professor in college--teaching a queueing theory class no less--claim it was 1/3 as long as you didn't care about the order, and I interrupted the class for a good amount to explain it was not.

jobigoud 5y ago
Are you sure this wasn't a variant of this problem where one of the result is already known? (Hence the "order" bit). There is a famous problem with endless debate about it, it goes like: a family has two children, one is a girl, what is the probability that the other one is a boy? Depending on the exact wording you can get 2/3 or 1/2. In your case say, A: let two coin flips, one is known to be tails, what's the proba of two tails? B: two coin flips, I show you one which is tail, what's the proba of the other also being tail? In the first case we don't care about the order and the answer is 1/3, in the second case we do and the answer is 1/2.
- jfengel 5y ago
  And that makes me take the study with a grain of salt. Probability problems are prone to different answers based on subtleties of phrasing and assumptions, like the famous Monty Hall problem. This question was, of course, pretty straightforward. But I suspect that with some further questioning, you'd find that they thought they were asking a different question than the one they were actually asked -- in very specific mathematical terms. Not being familiar with the way mathematicians pose questions is not the same as failing to grasp how probability affects your life. People are famously bad at judging risks, which are more important than the abstractions of flipping coins. And also much harder than flipping coins, since they depend so much on your assumptions and on the question you think your answering, as well as the difference between appetite for risk and your actual feelings about getting caught short. All of which is to say... a lot of people read this and said, "Aha, X is bad at math and therefore not to be trusted". Whereas I read those and say, "Aha, you are bad at understanding how questions work and how people think."
- dooglius 5y ago
  That may have been what he had in mind, but he made no indication as to there being a conditional probability. Furthermore, in the context of where he was going with it, I recall that there wasn't one either so he was getting the wrong answer as a result. He believed the not-looking-at-the-order was the critical thing making it 1/3 rather than 1/4.

jobigoud 5y ago

Are you sure this wasn't a variant of this problem where one of the result is already known? (Hence the "order" bit). There is a famous problem with endless debate about it, it goes like: a family has two children, one is a girl, what is the probability that the other one is a boy? Depending on the exact wording you can get 2/3 or 1/2. In your case say, A: let two coin flips, one is known to be tails, what's the proba of two tails? B: two coin flips, I show you one which is tail, what's the proba of the other also being tail? In the first case we don't care about the order and the answer is 1/3, in the second case we do and the answer is 1/2.

jfengel 5y ago
And that makes me take the study with a grain of salt. Probability problems are prone to different answers based on subtleties of phrasing and assumptions, like the famous Monty Hall problem. This question was, of course, pretty straightforward. But I suspect that with some further questioning, you'd find that they thought they were asking a different question than the one they were actually asked -- in very specific mathematical terms. Not being familiar with the way mathematicians pose questions is not the same as failing to grasp how probability affects your life. People are famously bad at judging risks, which are more important than the abstractions of flipping coins. And also much harder than flipping coins, since they depend so much on your assumptions and on the question you think your answering, as well as the difference between appetite for risk and your actual feelings about getting caught short. All of which is to say... a lot of people read this and said, "Aha, X is bad at math and therefore not to be trusted". Whereas I read those and say, "Aha, you are bad at understanding how questions work and how people think."
dooglius 5y ago
That may have been what he had in mind, but he made no indication as to there being a conditional probability. Furthermore, in the context of where he was going with it, I recall that there wasn't one either so he was getting the wrong answer as a result. He believed the not-looking-at-the-order was the critical thing making it 1/3 rather than 1/4.