I’ve got another one for you from our 5 lb. Book of GRE® Practice Problems, and this one’s serious. I took it from the Advanced Quant chapter. Try it out and then we’ll chat!
“Triplets Adam, Bruce, and Charlie enter a triathlon. There are nine competitors in the triathlon. If every competitor has an equal chance of winning, and three medals will be awarded, what is the probability that at least two of the triplets will win a medal?
© ManhattanPrep, 2013
Yuck. I’m not a fan of probability in general and this one is particularly annoying. Why? Because they ask for the probability that at least two will win. Most of the time, when a probability question uses at least or at most language, we can use the cool 1 – x shortcut because there’s only one not-included case.
For example, if I tell you I’m going to flip a coin three times, I might ask you to calculate the probability that I’ll get at least one heads. There’s only one case where I wouldn’t: zero heads. So you can just calculate the probability of zero heads and subtract from 1.
But we can’t do that here, because it’s possible for just 1 twin to win a medal and it’s also possible for zero twins to win a medal. Sigh.
Okay, how are we going to tackle this? Probability is a measure of the number of “desired outcomes” divided by the total number of possibilities. Let’s figure out the total number of possibilities first.
Take a look at the question again. Is this one of those questions where the order matters? If you don’t win, you don’t win. If you do win, does the question make a distinction between coming in first, second, or third?