Problem Set #1
I know you probably weren’t expecting this to turn into isomorphisms, but here’s a fun and exciting set of statistics problems for you to solve. Start off with the following assumptions:
- The city of Copenhagen can be divided into three bar-hopping zones: Amager, the city center, and everywhere else.
- In the city center, one-tenth of the bars are gay bars. Outside the city center, only one bar in twenty is a gay bar.
- Amager has no bars to speak of, because Amager blows.
- Bars outside the city center have decently cheap beer 2/3 of the time; bars in the city center have cheap beer only 1/3 of the time.
- Bars outside the city center have decent music 10% of the time; bars in the city center have decent music 20% of the time.
When I go out at night, I randomly choose a starting location, either in the city center, or outside of it. 80% of the time, the starting location is in the city center. I tried starting out on Amager once, but vowed never to do it again. Then I wander aimlessly, going into every bar I see until I find one that has both cheap beer and tolerable music. If I start out in the city center, I never leave, but if I start anywhere else I will walk to the city center with probability 0.1n, where n is the number of bars I’ve already tried that night.
- On average, how many bars will I visit each night I go out?
- So far I’ve found four bars I like. Two of them are gay bars, two of them aren’t, and all four of them are located within the city center. Given that in any non-gay bar there is a 25% chance of dodgy old (or young, but usually old) men making me ick out, and that gay bars definitely do not offer cheaper beer, what can be said about the quality of music in the average downtown gay bar?