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‘The roulette wheel has come red for the past seven goes. What are the odds of eight reds in a row? I’m betting on black.’
Humans are capable of quite accurately judging the path of a thrown ball, even without having studied Newtonian mechanics (not me, I can’t catch a ball from three feet away). However, as well documented, humans’ instinctual understanding of probability is very limited, amongst others, in terms of:
1. Neglecting Probability - When presented with alternative hypotheses, the go to answer is that they are all equally plausible. This is clear in the debates in the United States on evolution versus intelligent design. The intelligent design people say that both alternatives should be presented as equally plausible. However, not all hypotheses are born equal. Some are just better than others and evolution is better than intelligent design, which is not even a coherent idea. (A similar situation also occurs in the case of religious people, who do not allow for any chance of their hypothesis being false. However, this gets into a discussion on blind faith which can be left for another time.)
2. Being able to figure out which probabilities are applicable to a given situation - There are various ‘facts’ bandied about such as: You are more likely to die in a car crash than in a plane crash in your life. This is a truth on average. However, this includes a lot of people who have never flown on a plane or fly very rarely. If you fly frequently, this statistic is probably very different. Actually figuring out whether this is true is a lot more nuanced and is a function of distance flown and driven, routes flown (flying over an active volcano would probably be quite dangerous, I imagine) amongst other variables. Another famous example of this bias came out in American Footballer OJ Simpson’s trial on the murder of his wife. OJ had admitted that he used to beat his wife. His lawyer cited a study which showed that the probability of a person, who beats his wife, actually killing her is very low. However, this is the wrong probability to be looking for. Rather, the applicable probability is: Suppose a person beats his wife and then his wife is murdered, what is the probability that the husband did it. The fact that this flew in a court (albeit in an American court) shows the degree of this human bias.
3. Understanding when events are independent - This results in situations such as the one at the beginning of this article. As you can probably tell, the fallacy in the argument above is that past events of what happened on the roulette table do not effect the next event. A name for this bias is the ‘Gambler’s Fallacy.’ This is the reason why casinos make so much money. You have to be a complete idiot if you can’t afford to lose money and yet play games like roulette (unless you are Laplace’s Demon) or blackjack (unless you count cards) or flash (unless you are good at bluffing and/or reading people). This bias occurs in two ways as illustrated in the gambling analogy: a. I have lost so often. It must be my turn to win. b. I have been winning so much. I better ride my luck and continue playing.
4. Inaccurately calculating/estimating probabilities - One situation where this arises is in the case when a person is frightened. A spider is far less likely to hurt and kill us than getting into a car and driving. So, if you are frightened by a spider, you should be terrified of entering a car. However, most people ignore probabilities of events they take part in everyday or are slow moving and tend to overestimate less probable events. This is why heart disease is less scary than cancer to a lot of people even though they both have similar risks. This leads to people continuing with bad habits associated with heart disease.
There are many cognitive biases humans are prone to, and probability inevitably plays some role in those biases. As you can see from the examples given above, which are not close to indicative of the probabilistic biases present in humans, there is good reason that we need to get over them. Casino owners take advantage of this lack of education to steal money from those who can least afford it, courts and judges who are the guardians of justice and liberty are incapable of asking the right questions, students in the US are being subjected to misinformation and religious mumbo-jumbo, and our health priorities get skewed.
Another commonly cited example of our misunderstanding of probability is the ‘Monty Hall Game.’ If you haven’t seen it before, picture a game show with three doors. Behind one door is a car and behind the other two are goats (don’t ask me why). The assumption here is that you would prefer a car to a goat (for me it would depend on how hungry I was at the time). As the contestant you have no clue on which is behind which door. So, you are first told to select a door at random and not open it. Now, the game show host (who knows where the items are) opens one of the other doors with a goat behind it (there will always be at least one such door). The question is, should you switch doors to the other closed door or stay with the door you currently have? Why? Try thinking this through and watch the video below.
There are many reasons which have been suggested for our inability to understand and apply probability. One plausible story, put forward by evolutionary psychologists, is that humans had to make quick decisions to run away from objects they saw in the distance or run towards them in the case of hunting. This is a binary decision. The need of probability just didn’t arise, so humans never learnt to deal with it.
Whatever the reason, since these biases are so ingrained in us, just education on probability is not enough. This needs to be followed by education on critical thinking. However, most importantly, people must be encouraged to understand their natural biases, be mindful of situations when they might occur, and take a few seconds to contemplate other possible hypotheses and probabilities before taking decisions.
For more on this as well as on related topics, take a look at: http: //www.fallacyfiles.org/probfall.html Kahneman, Daniel - Thinking, Fast and Slow
(Madhav Kaushish is passionate about Mathematics and went on to major in Mathematics with High Honours from Oberlin College, USA. Madhav's thesis was in Number Theory, specifically Fermat's Last Theorem. Madhav is committed to spreading his love of Mathematics and has started SmarterGrades, an online, adaptive maths learning portal).
