I am currently studying for the GRE. Mostly, I am studying math. I have not studied math in approximately eight years.
I admit that I'm not terrible at math, but there's a reason I majored in History and French. There's also a reason I spend my free time writing as opposed to working calculations. But the time spent writing is creating interesting side effects when working story problems.
Specifically, I'm just not buying the authors of these story problems. Where's the motivation? Where's the conflict pushing these people to action?
For instance, this one:
Jack has a bowl of marbles. Six are blue, five are green, seven are red, and two are yellow. What is the probability Jack will pull a green marble if he selects one from the bowl at random?
Do you see my problem? Why in the world is Jack picking a marble from a bowl? For kicks? What kind of loser just wanders aorund picking marbles out of bowls? Even worse are the problems in which someone's friend asks him or her to pick a marble--what a bizarre way to spend time together. "Hey, want to see if you get a red marble?" "Sure!" "I'm glad we're friends."
Come on, test question writers. You can do better.
Jack is abducted by an alien spacecraft, and must participate in a ritual to determine if he will be allowed to return to Earth or not. The aliens have a large bowl filled with marbles--59 are blue, 27 are green, and 5 are red. If Jack picks a red marble, he will be executed. If he picks green, he can return to Earth. A blue marble means he will remain with the aliens indefinitely. What is the probability he will not be executed?
See? There are stakes! There's a reason for Jack to spend his time picking a marble, and consider the likelihood of each outcome. As for why the aliens use a strange game of chance to determine the fate of their abductees, I couldn't tell you, but who am I to judge alien societies' cultural norms?