Yesterday morning I ended up waiting for 30 minutes for a bus. According to the schedule, a bus should arrive at my stop every 10 minutes. That was the start of a particularly bad day for me.
Today, I woke up and felt like today was going to be better. I expect when I show up at the bus stop, it will be either right there or come within the first minute.
Am I doomed to disappointment?
I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Thursday, July 22, 2010
I Was Late for That First Meeting to Schedule the Meeting About the Conference
Posted by Unknown at 10:24 AM
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I love this problem, so many assumptions to make and so many ways to answer!ReplyDelete
I'll give one possible answer - assuming the timetable is correct and the buses arrive on time, then at any given minute a bus is either at the stop, or 9,8,7,6,5,4,3,2 or 1 minutes away from the stop - a total of ten different possibilities. So a bus being at the stop or one minute away is 2 out of ten possibilities, a 20% chance of meeting your expectation, or an 80% chance of disappointment.
Thanks for all these great puzzles!
reallyfatbloke, you're welcome.ReplyDelete
The arrival of the bus can be defined as a poisson process, while the time to arrival is on an exponential probability curve. In this case, the average (or expected time) till a bus arrives is 10 minutes. So the probability is about 9% that you will only have to wait for one minute or less for the bus to arrive.
The chances of waiting for at least 30 minutes is about 0.5%.
There's a good explanation of the two concepts here: http://cs.wellesley.edu/~cs199/lectures/19-exponential.html
I know, not exactly a brain teaser, but I find it interesting.