Thinking back to when I was an undergraduate, one of the homework assignments in a probability class was:

In a lottery, is it possible for the winning combination to be 1,2,3,4,5,6?

To paraphrase the lecturer's answer:

No, because the combination is very unlikely.

The official answer clearly is an error, but how does an undergraduate approach a lecturer when the given answer is wrong?

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    Btw, every combination is equally likely... – paul garrett Mar 1 '17 at 16:02
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    Is it possible you could have misremembered what was actually said? For instance, maybe the lecturer actually said that in a real lottery such a combination might not be used because some people are likely to pick something like this. I mention the possibility of misremembering because this is such an egregious error that I would think he/she would have gotten instant questions about this in class, or at least a huge number of student emails after class (assuming this was after email was in common use). – Dave L Renfro Mar 1 '17 at 16:18
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    @DaveLRenfro: Fair point. I'm quite sure I remember it correctly, but let's assume that the situation is as presented (i.e. how to challenge when a large error is made). – Bad_Bishop Mar 1 '17 at 16:34
  • As a student, I probably would have raised my hand in class and asked about it if a small class, say no more than 20 or 30 students, and I might have spoken to the teacher afterwards if a large class (and if I didn't think anyone else was going to say anything). As a teacher, I would have gotten several incredulous questions from students immediately in class, because in my experience in sometimes misspeaking, that's what happens when you inadvertently say something this incredible. However, student-teacher interactions are likely to be very dependent on the customs of where you are. – Dave L Renfro Mar 1 '17 at 16:46
  • If I saw someone make such an insanely mangled claim I would have close to no hope of any rational interaction with them thereafter. I might likely drop the course. (Not that I ever had a math instructor say anything so patently in violation of the terms being used.) – Daniel R. Collins Mar 1 '17 at 19:24

I have found the best way to handle that requires that first the student realize a few things:

  • the professor has a great deal of discretion to determine how to grade and mark things
  • professors are humans and make mistakes, and most are aware that misunderstandings and miscommunication can occur, and
  • like all other humans, being directly and publicly challenged or put in a position of being told "you are wrong" tends to evoke defensiveness which is rarely helpful to anyone in any situation

What I've found works the best for most situations is to meet the professor at an office hour or immediately after class (if they stick around for a few minutes), and ask about the issue. Go in with an open, learning attitude clearly wanting to understand - not trying to make a point or prove someone right or wrong.

To avoid defensiveness as well as allowing the person to "save face", you can put your question something like this: "I have a question about this homework problem, as I think I'm misunderstanding something." You are asking the professor for their help in understanding something important to the course, rather than framing it in a way of "defend your wrongness", and usually this results in a more pleasant conversation.

It can also be good to explain your reasoning clearly in answering the question, such as: "based on the principle we talked about in class a few weeks ago, of how all possible combinations of numbers are equally likely with a true lottery draw [showing you were paying attention to other things in class], I figured {1, 2, 3, 4, 5, 6} must be a possible outcome. I looked up combinations and lotteries in the textbook, and rechecked lecture notes, and I haven't found anything that indicated otherwise [shows you did due diligence in trying to figure out the problem without just asking, and thus aren't wasting their time]. Am I misunderstanding something?"

Then, the most important part: listen carefully to the explanation. If they don't explain and direct you elsewhere, such as to the book or part of a previous lecture, then make sure you have enough information to do that, such as indicating you absolutely will do that right away and, "just to make sure, we are talking about chapter X on combinations, right?" Then go do that.

If you don't find out you were mistaken, then take the materials back to the next meeting time and show them again. "I did what you advised and I read this part here in the book, which seems to support that the combination is equally likely. Can you please help me see where I'm going wrong?" Polite persistence is incredibly difficult to defend against, even for very cranky people.

Alternatively, you can be more direct and try to handle this in class respectfully. Doing this in class varies much more by professor, your developed social skills and attitude, your standing in class, and your local culture, but at least in my part of the US I've rarely had a problem. You just politely ask, at an appropriate time, to go over the homework problem, and ask for an explanation of what it is. If it contradicts what you thought you learned, then you bring it up and say so. "I thought that principle X meant that...how does that effect this problem?"

One or both of these methods has resolved every problem I ever had in classes that were worth the effort, and the remaining ones were so minor (a few points here or there) I just didn't bother if a the first thing tried (usually a quick question or asking for an explanation) didn't work. A more extreme situation might call for more, but that should only be after you tried all of the above and no resolution was reached of any kind, and the result is so dire to you that it's worth trying to go farther.

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    Another reason to be polite and approach it as "Please help me understand"---it's always possible, in principle, that you're actually wrong, and they're right. If so, this approach allows you to save face. – MissMonicaE Mar 1 '17 at 20:42

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