Probability for Kiddos and Would-Be Grad Students

I've just now been reading about the new question types on the GRE, including the "numeric entry" problems in which you actually type in the answer to a math question rather than selecting from the multiple choice list.

This was one of the example questions:

Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be one that is defective?

Give your answer as a fraction.

I know how to do this pretty easily using the hypergeometric distribution because I just took a probability course. It feels a bit tough for someone who hasn't, though.

Of course, I was surprised when working on that pre-algebra curriculum that questions just like this one appear in the book. (In an example I did not write myself, "Sally" was pulling single socks out of a drawer with replacement and another girl was drawing them with replacement.) Middle school students these days are expected to know quite a lot about probability (not just by this curriculum either - it's part of the "essential skills and knowledge" for Texas students), much more than I ever knew before college. I think this is a good thing.

However, less of a good thing is the fact that standard textbooks do not teach geometry using proofs. I was astounded by this, but apparently this shift happened about 8 years after I took geometry in 9th grade.

***While writing this blog post, a lens fell out of my glasses and I had to take it across the street to be fixed. It only took 15 minutes to get there, get the glasses fixed, and get back home, but the experience gave me this rush of renewed GRE paranoia -- great, there is yet another thing that could go wrong during the test. I have been mentally preparing for any number of disasters, but sudden blindness was not among them.