In the year 2034, Seattle has finished building an underground metro that serves the whole city. Susannah is a native Seattleite who lives in the middle of Capitol Hill and takes the metro to the grocery store every Sunday. The metro runs right underneath Broadway Avenue. There is a single platform in the middle that allows Susannah to get on a train in either direction. Susannah's train stop is equidistant from two QFC grocery stores, the one at Broadway Market and the one at Harvard Market. She arrives at the platform at a random time every Sunday. Both trains run every 10 minutes. She doesn't care which grocery store she goes to, but she is surprised to find out that she ends up going to the QFC at Harvard Market 90% of the time. Why is Susannah ending up at one grocery store significantly more often than the other?
####1. Why is Susannah going to the Harvard Market QFC most of the time?
Susannah ends up going to the Harvard Market QFC most of the time because the trains are timed such that the one going towards Harvard arrives at the platform one minute before the one going towards Broadway Market does.
####2. How did you arrive at that answer?
Let us assume that Susannah, who has no particular preference for one grocery store versus the other, simply gets on whichever train arrives at the platform first. The probability of Susannah getting on a particular train is dependent on the interval between the trains during which she would have to wait.
Extracting the ten-minute interval [0, 10], let us assume that the Harvard train arrives at minute [0], and the Broadway train arrives at minute [1]. Then, in order to catch the Broadway train, Susannah would have to arrive at the platform during the 1-minute time interval (0, 1]. However, if Susannah arrives on the platform during the 9-minute time interval (1, 10], then the Harvard train will be the next to arrive. Therefore, since Susannah is equally likely to arrive at any particular minute in the ten-minute interval, she will get on the Harvard train 9 times out of 10.
####3. What other possible explanations are there?
- It is possible that both trains arrive at the same time, but the way Susannah accesses the platform puts her closer to the subway door of the Harvard train than that of the Broadway train.
- Both trains could arrive at the same (or at 5-minute intervals, which would also imply an equal chance of getting on either train), but the northbound Broadway train is consistently more crowded, so Susannah opts for the less crowded Harvard-bound train.
- Susannah may be choosing to head towards Harvard Market because she has other errands in that direction.
- Susannah may not be able to see anything on the right side of her field of vision, which happens to be the side the Broadway train approaches, due to traumatic brain injury caused by rushing onto a subway train.