What are the odds of waking up in the middle of night and seeing exactly 3:33 on the alarm clock on your bed stand?

Let's assume that you normally go to bed and fall asleep around eleven in the evening and get up around seven in the morning when the alarm goes off.

That comes out to eight times sixty times sixty which equals 28800 seconds that you are sleeping.

In order to make the calculation simpler, let's also assume that you wake up only once in the night.

Therefore, the chance of waking up at exactly a given time (this case 3:33) is one in 28800 which equals 0.003472%.

Okay that may seem like a pretty good calculation, but wait. For those not paying close attention, I've made a fundamental error in my calculations.

Actually, the exact time of 3:33 is in minutes and not in seconds. So upon correction we've got eight times sixty which equals 480 minutes that you are sleeping.

One in 480 equals 0.20% which is a much greater possibility. Normally when I wake up it's not evenly spread across the whole night but usually between let's say 1:30 and 5:00, which isn't 480 seconds but is 210. One in 210 equals 0.47%.

Life is never what you expect it to be, and sloppy calculations make things much worse if you are too careless.