At 1:30, a student says, “if you do that probability 3 times, you ought to get that probability at least once.”

How should I have responded to this student? (I actually have the footage, which we can analyze at some point if we think that’d be fun.)

• It depends on the context which I don’t have, but most likely I’d have said something like “I have here a coin. What’s the probability of heads? Now I’m going to flip it. Oh, look, tails. What does that mean about the next flip?”

On the other hand, we’re really trying to get at the difference between “at least once” and “on average once”, so maybe my direction with that is not so good.

And there’s also the question of “ought to” — you do have a more-than-half chance of getting it at least once, so maybe the student’s statement is just fine. Hm.

Now I’m thinking I’d be more likely to say “What do you mean by ‘ought to get that probability at least once’?”

• Following up on Joshua’s comment – Have some conversations along the lines of ‘Is it possible to get heads four times in a row? Can you roll a die six times without getting a 1? Can you reach into a bag of M & M’s and get a certain color three times in a row?”
Obviously there is a desire to sneak in a conversation about limits and about how probability is just a shortcut to discussing long range likelihood, but the more concrete examples are meaningful ones.

• Julie

Thanks for letting us into your room! Loved how you utilized experimental probabilities to begin their thinking around the theoretical. Obviously we aren’t seeing everyone. I think I would have asked the student to restate their idea for clarity/precision. Which probability? Do we ‘do probabilities’? I think his language was misleading which could mask a misconception we can’t really know based on his statement.