One of UC Berkeley statistics professor Deborah Nolan's favorite classroom activities involves coin flipping. She splits students into two groups, and asks both to write the results of 100 coin tosses on a chalkboard. The catch? One group actually tosses the coin, and one group just writes what they think the results would be. When Professor Nolan returns, she's always able to identify the group that actually tossed the coin, because their results are always littered with seemingly improbable streaks that the other group would have never thought to write down—despite the fact that they're university-level statistics students. This is one demonstration of the law of large numbers: even though a coin always has a 50 percent chance of landing on heads, in five tosses of a coin, you might come back with a streak of four heads. But if you toss that coin 50, 100, or 1,000 times, the average of heads to tails gets ever closer to that true 50 percent probability.
Take a look at the picture below. Can you guess which box is the result of real-life coin tosses, and which box represents someone's guess of what the result of 100 coin tosses might be? It's a quick exercise in the science of chance.
A Quick Coin Toss
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Key Facts In This Video
Stochasticity means randomness, which can be thought of as unpredictability happening within a set of predictable rules. 00:08
An experiment at UC Berkeley had one group of students flip a coin 100 times and write down the results, and another group simply write down what they think the results of 100 coin tosses would be. A statistician looks at both results and knows which team actually flipped the coin, because the real results show patterns that don't show up in the fake results -- long stretches of only tails, for instance. 00:35
In a stochastic system, you can never predict the exact results, but you can forecast the probability that certain sequences will show up. 01:20