Randomness

Although not directly related to personal finance, randomness very much affects short-term financial performance and therefore, influences our financial decisions (and arguably pretty much everything in life!).

Random walk theory says that it is impossible to predict how a stock will move at any given time. In the short- and medium-term, a stock's price doesn't have any known relationship with either its intrinsic value or the value of any other assets on the market.

The following example (really, a puzzle) is not related to personal finance but illustrates an important point about chance or probability. I recently read the book about this subject called Fooled by Randomness by Nassim Nicholas Taleb that led me to another interesting book: Randomness by Deborah Bennett.

In the latter book, the author Deorah Bennett writes: “To even the mathematically enlightened, some issues in probability are not so intuitive.”

She then uses the following example from the psychologists Daniel Kahneman and Amos Tversky to illustrate this point:

A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data:

(a) 85% of the cabs in the city are Green and 15% are Blue.

(b) A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.

What is the probability that the cab involved in the accident was Blue rather than Green?

If you enjoy solving mathematical puzzles, you may want to pause here and see if you can solve this problem correctly.

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She continues: A typical answer is around 80 percent. The correct answer is around 41 percent. In fact, the hit-and-run cab is more likely to be Green than Blue.

To reiterate, even if the witness identified the offending cab as Blue, it is more likely to be Green (59%) than Blue (41%)!

However, she does not provide the explanation of the correct answer. So, here it is:

Probability that the Blue was involved (based on % of cabs)	15%
Probability that the Green was involved (based on % of cabs)	85%
Probability that the Blue was involved, and witness correctly identified cab as Blue (15% * 80%)	12%
Probability that the Green was involved, and witness incorrectly identified cab as Blue (85% * 20%)	17%
Therefore, probability that the Blue was actually involved when witness identified cab as Blue (12% / 29%)	41.38%

As to why most people answer 80%, here’s the possible explanation:

Kahneman and Tversky suspect that people err in the hit and run problem because they see the base rate of cabs in the city as incidental rather than as a contributing or causal factor. As other experts have pointed out, people tend to ignore, or at least fail to grasp, the importance of base-rate information because it “is remote, pallid, and abstract,” while target information is “vivid, pressing, and concrete.”