Friday, March 11, 2011

Coincidently Dependent

Is it a coincidence, statistically randomness or mysteriously some like of predestination? Is De ja vu a mind experiencing some kind of electrical anomaly of memory?

The mind likes the logical connection of what may just be the natural probabilities of two independent (or dependent) events being correlated. We love to create cause and effect truths.

As a statistician, I have studied probabilities and the field of uncertainty with intensity. Yet each time I recall the theory I continue to combat the mind's tricks of mis-estimating, emotional forecasting and creating logical patterns of cause and effect.

So here is an example. What is the probability in 20 coin tosses that there will be 5 heads in a row? Well, last night I tried it four times. I had many 3 in a row, but no 4 or 5 in a row. Yet the probability is 25% - somehow higher than I would have predicted.

If I asked what is the probability of 20 heads in a row in one try at 20 consecutive tosses most would say it is infinitesimal (9.35674E-07). It's easier to think of this in terms of 1 chance in how many outcomes. Flipping a coin 20 times has 1,048,576 combination's (2^20).

We are all poor judges of uncertainty (even the best statisticians get fooled). We understand conceptually the small probability of 20 heads in a row but always must remind ourselves that on the 20th toss the probability is still 50% of getting one more head regardless/independent of the pattern of heads on the prior 19 tosses (very important fact when gambling at roulette).

Complexity with probabilities always comes when the events are dependent. Coincidentally nearly every event in human interaction is dependent.

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