Thursday, 5 April 2012

Tuesday Night's Stats Lesson

GHOST/ECHO was pretty amazing on Tuesday night, another great example of a wonderfully complex story being built up from simple pieces collaboratively. That was one of two amazing things that happened on Tuesday.

The second was when someone (I feel like I should protect his identity) rolled three d6s and said, "Wow, look at that!" He had rolled three 6s. Which is quite amazing - but more amazing was the comment that followed next from him: "There's only a 1 in 18 chance of that."

My head snapped around like Linda Blair. "Whaaaaaat?!" I cried. "1 in 18? 1 in 18?!!!"

"What? What's wrong?"

Sigh. What do they teach people these days?

If two (or more) events are independent - meaning that one has no bearing at all on the other (and vice versa) - then we can take the probabilities of these two events and simply multiply them together. So if we had a coin and a d6, and wanted to know the probability that upon flipping and rolling them we got a Head and a 5, we would take the two probabilities (1/2 and 1/6 respectively) and multiply them together to give us 1/12. Job done.

The same holds true in this case for our three 6s. For all intents and purposes we can assume that they do not affect each other. So rolling three 6s is (1/6) times (1/6) times (1/6) or 1/216 in total. If you're a percentage kind of person that means there's slightly less than a 0.05% chance of rolling three 6s. 1 in 18 is around 5.5%.

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