Public Radio Pledge Drive Probability

North Carolina Public Radio Pledge Drive Season is the worst time to miss a call from an unfamiliar number. I have missed several such calls in the past few weeks, and I am convinced that each one was Eric Hodge. He was calling to inform me, via vague, leading questions about famous landmarks and culturally-specific foods, that I'd won a drawing for one of the fantastic getaways they always advertise. One of these days, I'll be right. But which one of these days?

It's a little tough to figure out how likely I am to win any particular WUNC Trip Drawing. My probability of winning is always nonzero, since I'm a Sustainer, which means I'm a) better than everyone else and b) automatically entered into every Pledge Drive drawing. The amount of funding that North Carolina Public Radio receives from listener contributions is public knowledge, but the precise number of contributors isn't listed anywhere that I could find. Even if I could figure out how many Sustainers there are, the number of one-time-gifters in the pool changes with every drawing.

There are a couple ways I can estimate how many people listen to WUNC, which is a good start for figuring out how many people are competing with me for that weekend getaway in France. This Nielson report from December of last year indicates that 90% of Americans listen to radio each week, and the Raleigh-Durham region has a population of about two million, so the local radio-listening audience is probably somewhere around 1,800,000. WUNC's weekly cume is a little under 17% of the market, so there are probably at least 300,000 people tuning in each week. Maybe. Man, I hope I'm estimating radio listenership the right way, since it's sort of my job that I get paid for!

So, let's be optimistic and assume that maybe one out of every twenty listeners donates to the station. I've got no clue if that estimate is wildly high or wildly low or wildly spot-on, never having worked for an organization that depends on donations, but it feels like a vaguely educated guess. That's 15,000 donors total. It probably fluctuates, but let's say, for argument's sake, that I have a 1 in 15,000 chance in any given drawing of winning a trip to Rome. There are three WUNC Pledge Drives each year, and each one seems to have at least five trip drawings, so I have fifteen chances each year to win.

How long would I have to wait before I could be at least 90% sure of winning at least one trip drawing? Put another way, how many times do I have to enter a drawing so that my chance of losing every single last of them dwindles to 10% or less? My chance of losing any individual drawing is 14999/15000, and my chance of losing all the drawings I enter is 14999/15000 raised to the power of the number of drawings in which I participate. So let's solve this equation!

The sooner I get LaTeX on my new computer, the better

Using the definition of a logarithm and the change of base formula, both of which I totally remembered and did not need to look up just now, because I am a smart mathematician who never ever forgets really basic important facts, and being chronically rusty on logarithms definitely isn't a significant source of anxiety for me, we conclude that the number of drawings I'd need to enter in order to have a 90% chance of winning at least one of them is... 34,538 drawings, or over 2,300 years worth of pledge drives. Lucky for me, my loyalty to quality radio programming is as undying as the sun. Which means, strictly speaking, not actually undying. But undying enough to last for 2,300 years.

This one isn't about statistics, but is instead about my mom, and her death

I feel very sad, very often, and very little remedies the sadness.

I've started writing this thing so many times, and discarded so many drafts. If I took all the words I've written and deleted since December 7th 2013 and put them together, I'd win NaNoWriMo. Sometimes what I wrote was eloquent, but most of the time it was impenetrable garbage that rambled on way past the point where it stopped making sense. Sometimes what I wrote was angry, and mostly it was angry at people who had nothing to do with what I was angry about. Sometimes it had a lot of science in it. Sometimes it used a lot of metaphors. Sometimes it included a lot of fandom references. Sometimes it had pictures, and sometimes they were pictures that I drew (poorly). Sometimes I was bitter. Sometimes I wrote while I was sober, sometimes I wrote while I was drunk, and sometimes I wrote while I was crying and couldn't stop.

Mostly, all the things I wrote were just different ways of saying the same thing: My mom died. I feel very sad, very often, and there are very few things that remedy the sadness. Writing isn't one of them.