It turns out one of my favorite newer West Wing characters, Elsie Snuffin, who I think of as "Will's smarter sister", is a math geek in real life, with a published proof to her credit. She even has a math section on her official fan site, where she answers fan's questions with discursive, tutorial-style answers.
Q: I think you are great on "The West Wing"! Heres my current problem, its in advanced finite math (Im a high school senior): At the height of the Beatles’ popularity, it was estimated that every popular music station played their music 40% of the time. If you tuned through 10 such stations at any given moment, what is the probability that at least *one* of the stations would be playing a Beatles song? Thanks!
Danica Answers: A probability question! Okay, let’s call "x" the probability that "at least one of the 10 stations would be playing a Beatles song at that moment." That’s what we’re asked to find. Then let’s call "y" the probability that "none of those 10 stations would be playing a Beatles song at that moment." Notice that x+y = 1.... Okay, so we’ll now determine the value of "y" which is much easier than going through all the necessary calculations required to determine "x" directly. This is a common strategy in probability....
I am so amused.