Most common answers on the SAT

pckeller
Mon, 14 Mar 2011 19:44:34 +0000

Nothing too nerdy about this at all! Some related nerdery: pick up any section, look at the answers and you will find things like: 12 in a row with no ‘d’, only 2 e’s in an entire section…other similar weird stretches – and these are all completely normal. People just don’t expect weird sequences as often as they come up.

I forget where I read this, but it seems related: ask half the students in a class to flip a coin 100 times and record the results, while the other half just pretends to flip coins, but actually just makes up a random string of 100 h’s or t’s. Then examine the data. You can usually tell who did the experiment vs who faked it. The fake data doesn not have as many weird strings: runs of lots of h’s in a row say. For example, 5 in a row seems unlikely, but in a random set of 100, it is actually more likely than not to have at least one such stretch.

Of course, that leads to a probability question, too hard for the sat: you flip a coin 100 times. What is probability that you do not get at least one stretch of 6 h’s or 6 t’s in a row?