You are walking down the hallway when you run into your lab partner walking in the other direction. The two of you first step one way and are still in each other’s way. Then you both step the other way and are still in each other’s way. Then you both wait a bit, hoping the other person will step aside. You can model this situation as a metastable point and apply the same theory that has been applied to synchronizers and flip-flops. Suppose you create a mathematical model for yourself and your lab partner. You start the unfortunate encounter in the metastable state. The probability that you remain in this state after t seconds is e ^{– t/τ} : τ indicates your response rate; today, your brain has been blurred by lack of sleep and has τ = 20 seconds.
(a) How long will it be until you have 99% certainty that you will have resolved from metastability (i.e., figured out how to pass one another)?
(b) You are not only sleepy, but also ravenously hungry. In fact, you will starve to death if you don’t get going to the cafeteria within 3 minutes. What is the probability that your lab partner will have to drag you to the morgue?