# Probability

## 3. A Series of Unfortunate Unlikely Events

So far, we've only looked at single events: a single lottery draw or a single hand of poker. What about a series of events? A common creationist tactic is to take a long list of events, assume that they had to occur simultaneously, and then declare that the odds against such an occurrence are astronomically high. This is a quote from a typical creationist argument:

"Proteins are functional because the amino acids are arranged in a specific sequence, not just a random arrangement of left-handed amino acids. The formation of functional proteins at random could be likened to a monkey trying to type a page of Shakespeare using the 26 letters of the alphabet. Anyone knows that the monkey is not capable of accomplishing the task set before him."

That's a pretty impressive argument, right? It's been estimated that it would take longer than the age of the entire universe for a monkey to actually type a page of Shakespeare. But this argument contains a hidden assumption: that the entire page has to be typed at once, or that the entire amino acid sequence has to be assembled at once. What if you can build it piece by piece? What if our hypothetical monkey is allowed to keep typing letters until they assemble a word in the sequence, and then goes on to the next word? Does that change the odds?

As it turns out, it changes the odds tremendously. In order to illustrate this, let's go back to the world of gambling and look at a familiar object: dice. Now I know what you're thinking: you're thinking "This guy has an obsession with gambling. Maybe he should seek help." But leaving my personality flaws aside, let's consider the problem of rolling dice. Specifically, rolling 10 sixes. If you took ten dice in your hand and rolled them, how likely are you to get ten sixes? That's a pretty simple calculation: there are 6^10 possible combinations, so your odds are 1 in 60466176. Of course, you can always try it yourself. The following JavaScript widget will roll dice for you until you get ten sixes:

Did you try it? How long did you wait? At 2 rolls per second and more than sixty million combinations (since the widget keeps the dice in order), you might get lucky in roughly ... one year. Assuming you don't want to wait that long, hit the "Stop" button and try this new widget, which does the same thing but does it one die at a time instead of trying to get them all at once:

That didn't take too long at all, did it? So what was the difference? The difference is that when you have a series of events, there is really no need to assume they all happen simultaneously. You can take them one at a time, adding on sequentially. And when you do so, the odds collapse to relatively tiny numbers because you no longer multiply them together: instead, you add them one at a time, as they happen. So your odds of getting the first six are 1 in 6: something that should take only a few seconds. Then your odds of getting the next six are also 1 in 6, which should also take only a few seconds. On average, you're probably looking at around 30 seconds to get all ten sixes, as compared to a year the other way.

### So what did we learn?

When you consider the huge difference between treating sequential events as a series as opposed to a single simultaneous event, you begin to realize just how easily creationists can exaggerate the unlikelihood of series events in evolution, even if we assume that these events are completely random.

Now consider the famous "monkeys typing Shakespeare" argument. If we modified our little die-rolling widget to roll for letters and select good letters, what effect do you think that would have on the time required to reach the goal? Perhaps our monkey should start practising his typing.

### Acknowledgements

• The forum user "IPeregrine", for content suggestions.
• Rob Dalton and forum users "Darth Holbytlan" and "Starglider", for debugging assistance.

Continue to 4. Examples of Non-Random Probability

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