Unlikely events happen, but what are the consequences?
So far we’ve looked at how probabilities tell you how likely certain events are. What probability doesn’t tell you is the overall impact of these events, and what it means to you. Sure, you’ll sometimes make it big on the roulette table, but is it really worth it with all the money you lose in the meantime? In this chapter, we’ll show you how you can use probability to predict long-term outcomes, and also measure the certainty of these predictions.
Have you ever felt mesmerized by the flashing lights of a slot machine? Well, you’re in luck. At Fat Dan’s Casino, there’s a full row of shiny slot machines just waiting to be played. Let’s play one of them, which costs $1 per game (pull of the lever). Who knows, maybe you’ll hit jackpot!
The slot machine has three windows, and if all three windows line up in the right way, the cash will come cascading out.
This sounds like something we can calculate. Here are the probabilities of a particular image appearing in a particular window:
The three windows are independent of each other, which means ...