There are two boxes and both have red and black balls inside.

Box **A** contains 100 balls: 50 red and 50 black.

Box **B** also has 100 balls, but you don’t know how many are red and how many are black.

If you choose one of the boxes without looking inside and draw out a red ball, you win Rs. 10,000.

Which box will you choose: **A** or **B** ?

**A** or **B** ?

You have probably chosen **A**.

If so, you are not the only one. Majority does go for **A**.

**Let’s play it again, using exactly the same boxes.**

This time you win Rs. 10,000 if you draw out a black ball.

Which box will you go for now? **A** or **B** ?

Which one ? **A** or **B** ?

If I am not wrong, you have again chosen **A**.

But then, don’t you feel that the second choice was illogical – in the first round you chose **A** assuming **B** to contain fewer red balls and more black balls. So rationally, you should have opted for **B** second time.

Don’t worry.

You are not alone making this error.

Most people commit this mistake which is known as the Ellsberg Paradox – named after Daniel Ellsberg, a former Harvard psychologist.

Ellsberg Paradox offers empirical proof that we favour known probabilities (Box **A**) over unknown ones (Box **B**). It is generally taken to be an evidence for ambiguity aversion, in which a person tends to prefer choices with quantifiable risks over those with unknown, incalculable risks.

This brings us to risk and uncertainty or ambiguity, and difference between these.

### Risk

Risk means that the probabilities are known. In simple terms, risk is the outcome of an action taken or not taken in a particular situation, which may result in loss or gain. It is termed as a chance or loss or exposure to danger arising out of internal or external factors, that can be minimised through preventive measures.

Risk implies quantification or estimation of likely losses and is directly proportional to hazard, vulnerability and exposure and inversely proportional to capacity. Risk is perceived differently by people based on their occupation and skills, and perceived level of risk varies with socio-economic condition of the population.

The meaning of risk is not much different even in the realm of financial world. It implies uncertainty regarding the expected returns on the investments made i.e. the probability of actual returns may not be equal to the expected returns. Such a risk may include the probability of losing a portion or whole investment.

Systematic and unsystematic risk are two major components of risk, which when combined result in total risk.

Systematic risk is a result of external and uncontrollable variables, which are not industry or security specific and affect the entire market leading to the fluctuation in prices of all the securities. This includes interest, inflation, and market risks.

Unsystematic risk refers to the risk which emerges out of controlled and known variables, that are industry or security specific. This includes business and financial risks.

### Uncertainty

Uncertainty or ambiguity means that the probabilities are unknown. In simple terms, uncertainty implies absence of certainty or something which is not known. It refers to a situation where there are multiple alternatives resulting in a specific outcome, but the probability of the outcome is not certain. This is because of insufficient information or knowledge about the present condition. Hence, it is hard to define or predict the future outcome or events.

Uncertainty cannot be measured in quantitative terms through past models. Therefore, probabilities cannot be applied to the potential outcomes, because there exists little or no data on the outcome of past occurrences.

**Risk v/s uncertainty**

The term risk and uncertainty are often mixed up and even used interchangeably, but the difference between the two needs to be understood.

- The risk is defined as the situation of winning or losing something worthy. Uncertainty is a condition where there is no knowledge about the future events.
- Risk can be measured and quantified, through theoretical models. Conversely, it is not possible to measure uncertainty in quantitative terms, as the future events are unpredictable.
- The potential outcomes are known in risk, whereas in the case of uncertainty, the outcomes are unknown.
- Risk can be controlled through proper and planned measures while uncertainty is beyond the control of the person or enterprise, as the future is uncertain.
- Minimization of risk can be done, by taking necessary precautions. As opposed to the uncertainty that cannot be minimised.
- In risk, probabilities are assigned to a set of circumstances which is not possible in case of uncertainty.

Let us look at two examples: one from medicine where probability works and one from economy where it does not.

There are billions of humans on earth. Our bodies do not differ dramatically. We all reach a similar height and a similar age. Most of us have two eyes, two ears, four heart valves, thirty two teeth. Another species would consider humans to be homogeneous – as similar to each other as we consider mice to be.

For this reason, there are many similar diseases and it makes sense to say, “There is a 30% risk that you will die of cancer.”

On the other hand, the assertion that, “There is a 30% chance that the euro will collapse in the next five years” is meaningless because economy resides in the realm of uncertainty. There are not billions of comparable uncertainties from whose history we can derive probabilities.

**Tolerate ambiguity**

Statistics is an age old science of risk and a number of researchers routinely deal with it, but not a single textbook exists on the subject of uncertainty. Because of this, we try to squeeze ambiguity into risk categories, but it does not really fit.

On the basis of risk you can decide whether or not to take the gamble.

However in the realm of uncertainty, it is much harder to take decisions.

To avoid hasty judgement, you must learn to tolerate ambiguity. This is a difficult task and one that you cannot influence actively. Your amygdala plays a critical role. This is a nut sized area in the middle of the brain responsible for processing memory and emotions. Depending on how it is built, you will tolerate uncertainty with greater ease or difficulty. This is evidence not least in your political orientation: the more averse you are to uncertainty, the more conservatively you will vote. Your political views have a partial biological underpinning.

Either way, whoever hopes to think clearly must understand the difference between risk and uncertainty. Only in very few areas can we count on clear probabilities: casinos, coin tosses and probability textbooks. Often we are left with troublesome ambiguity.

So learn to take it in stride.

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