Probabilities vs. Possibilities – The Red Marble Experiment

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I recently came across an experiment where participants are asked to choose between two urns, one containing 10 marbles (Urn A), of which 1 is red, and one containing 100 marbles (Urn B), of which 8 are red. If the participant draws a red marble at first trial, then he/she wins a prize. This is the simple version of the experiment. Which one would you choose?….

Well, the probabilities are clear. You have more chances to be a winner if you choose to draw from the small urn (10%) rather than drawing from the big urn (8%). However, experiments showed that 30%-40% of the participants opted for the large urn B, and this is called Ratio Bias (Dale et al., 2007) or Denominator Neglect (Kahneman, 2012). Researchers believe choosing the second urn is irrational (hence, wrong or worse decision) and that this is one of our many mind fallacies.

It is well evidenced and experienced that our brain is prone to errors. Our intuitive impressions of the world often lead us to wrong answers. Only by recruiting our rational thinking we increase the probabilities of taking the right decision. However, in such a case as this of choosing between the two urns, I think our intuition is correct, even though this is statistically (rationally) wrong.

The reason is that statistics do not apply at the unit, the one person or the one incident. Probabilities are stating how many winning trials are possible out of one hundred trials, but they in no way can tell you at what order successes will come. Statistics work only at large numbers. This is how, for example, insurance companies do business. They use probabilities successfully and in a lucrative way, but they do not insure only one person, they insure thousands.

Back to the experiment, when someone is asked to pick a marble, the winning red may come at first trial, at fifth trial, at sixtieth trial (if they are 100 in total) and so on. If doing this many times, the order will always be different, as the inherent natural randomness dictates. But, at the isolated unique incident we just do not know. Regardless the background (i.e. how many marbles are in total), the bottom line is that in urn A one red ball is sitting there waiting to be picked at first attempt, and in urn B eight red balls are waiting in the line of randomness. So, the probability is lower (8% vs. 10%) but the possibilities are higher (8 vs. 1).

Going deeper in the argument, quantum theory suggests that the observer affects the observed result (at the quantum level) just by observing, in that the outcome depends on perception. The act of picking a marble, or else making a choice, is just a cloud of different possible outcomes. In theory, we can affect the observed result, or else we can choose our “universe”, and everything is possible since the outcome is not real until we measure it or observe it.

The material world is an expression of an infinite number of individual instances or possibilities, and it can be predictable to a certain extent, when speaking for a relatively infinite number of individual choices. This is what we call probabilities. But when we regress to the individual event, things change. We then have to do with possible alternatives. In the present experiment we may opt to see between 8 possible winning outcomes at our first observation against only 1. The density of the possible positive results (successes) is larger.

In probabilities, the total number of all possible outcomes (successes and failures) is taken into account. The winning trial(s) is a proportion of that number. But, as we said, nothing is real until it is measured. In that sense, probabilities in the urn experiment will become reality only when we have picked all the marbles out of the urn. In possibilities, the number of expected individual successes is what counts most. We don’t care about the failure results. The density of the “winners” streaming in the pipeline of the unique trial’s possible outcome is more important than their probabilities to become real (to be observed) within a background of a total of possible events. The formulas and the examples below (Appendix 1) illustrate my point. Every time we try for a desirable outcome, the same possibilities equation applies, because each new trial is considered as an isolated unique event taking under consideration the possible successes.


Dale, D., Rudski, J., Schwarz, A., Smith, E., 2007, “Innumeracy and incentives: A ratio bias experiment”, Judgment and Decision Making, Vol. 2, No. 4, pp. 243-250

Kahneman, D., 2012, “Thinking, Fast and Slow”, Penguin Books, London

Download the full article in PDF here

Appendix 1

Possibilities vs Probabilities

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