Friday, November 30, 2012

Q: Event A has a probability of 70% of happening within the year and event B, 40%. The events are independent and uniformly distributed through the year. What is the probability that they will occur within 3 months of each other?

There is more than one way to answer this question!

The ambiguity comes down to exactly how we interpret the statement that "Events A and B are uniformly distributed across the year."

FIrst interpretation: Events A and B are produced by a memoryless process with uniform hazard function. Every day, we wake up and Event A has a certain uniform probability of happening that day, the same as every other day. Event B is independent and has its own uniform probability of happening that day. If the event doesn't happen, we go to bed and wake up the next day, and it's the exact same story, with the same probabilities, all over again, just like "Groundhog Day."