[rebkilde]

Last week, when I stopped at our small market, there were eight cars filling all eight spaces, and they were all silver. Is it possible to figure out what the probability is that this would happen? How would you go about figuring this out? It seems like it would be kind of complicated. I'm not a mathematician and this is not a homework problem, but I would love to hear about how a smart person would figure this out. Thanks!

[jcaron2]

First you need to know what portion of all the cars in your area are silver. You might be able look it up somewhere, or you could just hang out at an intersection or freeway overpass and count them. Let's say it turns out that 22% of the cars are silver. That means there's a 22% chance that the car in the first space will be silver. There's also a 22% chance that the car in the second space will be silver. However, the chances that BOTH will be silver are 22% x 22% = 0.22 x 0.22 = 0.0484 or 4.84% chance. The chances of three cars in a row being silver are 0.22 x 0.22 x 0.22 = 0.010648 = 1.0648%. The chances of 8 cars in a row all being silver are 0.22^8 = 0.0000055 = 0.00055% or a little over 5 chances in a million!

Of course, my number of 22% is purely made up. I have no idea what the real portion of silver cars is; that's just an example. But that's how you'd calculate it.

[Unknown008]

And remember that while this might be rare, it might also be rare that you have other cars of different colours parked in some particular order. So all in all... that event might be rare, but that doesn't mean that it'll never happen, as it is the case with other events involving probability, unless you have 0 or 1. :)