Of Uncertainties and Probabilities

Asks Prof. Ethan Mollick: I have a spinner, when I spin it, 30% of the time it lands on red, 70% of the time it lands on green. I spin it. What color does it land on, red or green?

It's interesting to observe that many netizens chose green. After all, it has a high likelihood.

But what many seem to forget is that one cannot predict the outcome of a single spin. The Law of Large Numbers (LLN) alludes to the outcome approximating green, on average, if there's plenty of trials run. (A commenter on the LinkedIn post even shares a Python code simulating LLN, thus answering 'green' to Ethan's question focusing on a single outcome: "I spin it."

If we calculate the entropy of this binary system, it's 0.8813 bits, very close to the maximum entropy of 1 (attained when the probabilities of random events are equally likely). In other words, it is fairly uncertain (or random) with a slight bias toward green. Even with an entropy close to zero, we would still be unable to predict the outcome of a single spin, since they are still subject to chance. We would, however, be very surprised if the outcome were a very low-probability event (high information) compared to the expected event (low information).