Now I suspect most of the class is too lazy to toss a coin a hundred times. It's likely a lot of them will simply write out what looks like a random sequence of Hs and Ts and turn that in.
But I am almost sure that, with a quick look at each submitted sequence, I will be able to tell which ones were produced in this fake way, and which ones are actually a faithful record of a hundred coin tosses.
How do I tell the fake sequences from the genuine ones?
(Thanks to my charming cousin for reminding me of this last month.)
Kovendhan has a comment with the right answer: "In order to appear genuine, students will avoid long sequences (6 or more) of consecutive heads or tails. In reality, such long sequences almost always occur in long trials."
Which of course begs the bonus question: in a sequence of 100 coin tosses, what's the probability that there will be at least one sequence of 6 heads or tails?
All right, bonus question #2: what if I changed the "6" immediately above to "6 or more"?