Probability of 'Going Standby'

Today's weather: High = 22 Low = 13
Mostly Cloudy

Going standby would apply to taking a road test (in my case), catching a flight, or a variety of situations where you are literally standing by and waiting for someone who is late for their appointment, cancels, or doesn't show up.

The math for calculating a success in 'standing by' is actually very simple and intuitive. It turns out that people who haven't studied math can easy figure this out by common sense anyway, but I'll throw in a calculation just for kicks.

Let 'x' be the percent chance that a person shows up for an appointment, and 'n' is the number of appointments in a given day.

For a total of 'n' appointments, then we have x^n (x to the power of n) chance that everyone shows up for their appointments.

For an arbitrary example, suppose x = 90%, which is something I pulled out of hat, but it seems reasonable. You always hear about how planes have a 10% no-show rate for booked tickets, so that's where I'm getting it from

The 'success' that we're really interested in is the negation of everyone showing up for the appointment. That is, simply put, 'at least one person doesn't show up' is success.

The function we can use to represent that is y = 1 - x^n which is a reverse exponential.

For a sufficiently large number of appointments in the day, then the chance of success approaches 100% in the limit. In other words, the 'y' value of the function approaches 1

Keep in mind this function is CUMULATIVE. So that just means that the longer you wait, the closer you are to 100% success, which will happen more likely towards the end of the appointments.

But in order for this to work, you have to start at the beginning, which means you MUST get their early and be the first or second guy in line. The calculation says you'll probably have to wait for a large number of 'n' to take place at first, but you have to stay put just in case your 'n' comes up early.

So it's a forced waiting game, but the longer you wait, the better your chances.

The calculation is more complex if there arepeople waiting ahead of you in line, but it works out exactly as the non-math people would say: your chances get very slim.

That's why you have to bust your butt out there and be the first one in line no matter what. The Chinese would be the first to tell you that anyway, as they live by that motto.