Probability on the SAT

What’s more likely, getting heads three times in a row on a coin toss or rolling snake eyes in dice? (Snake eyes is two 1’s . . .)

What’s more likely, getting a girlfriend this week AND passing your math test or getting a girlfriend this week OR passing your math test?

Probability can be a *&^%$. Seriously. 

And that’s the point of today’s lesson. I will very briefly break down probability on the SAT. After the break, I will talk about this blog, a neat probability story, and other adventures.

Probability does not have to be hard

A common issue students have is not knowing WHERE to put WHAT. Often times, the denominator in a probability problem feels impossible to find out. But that really is the SAT pulling a fun mind game on you. If I say, there are five people sitting at a table (a, b, c, d, e) and I want to know the probability of C and D sitting next to each other, you start to freak out.

And freak out you should. But think about it, what is the denominator? What is the total number of ways those five fools can sit together? It’s 120!! But how did I get that? Easy, you don’t need some complicated formula, it’s just 5! … 5 * 4 * 3 * 2 * 1

There is this neat counting problem I ask during my course, it goes something like this:

If P is the unique combination of letters possible with the five letters of VIRGO and Q is the unique combination of letters possible with FOUR letters in VIRGO, what is (P^2 – Q^2)?

Now look, I admit that question is a bit iffy, and it’s probably not even close to an SAT question, but I ask a variation of it to get a few points across. (1) The SAT is never that hard and (2) Most of the math can be solved without a calculator. I realize that P = 120, because 5 * 4 * 3 * 2 * 1. But now I’m being asked to square 120. I don’t want to do that, because that sounds hard. So instead, I’ll just look into Q. It turns out that Q = 120 as well, because 5 * 4 * 3 * 2 = 120. So, and this is the thing, it was a trick question. I don’t have to square 120, I just have to realize that P = Q. The SAT is like that on many questions.

Which leads me to my point. There are many different ways to solve an SAT problem. There is no one right way to solve any particular problem. The best chance you have is to learn all the knowledge required, master the strategy for the SAT, and perfect your SAT pacing. Then, life is gold.