We need to recruit a junior manager for our retail department. We know that a lot of people are qualified for this job, equally men and women. Today, we are suppose to meet ten candidates. This morning, we have met six female candidates.
What are the most probable genders of the next candidates, in the order of arrival?
As there is a lot of potential candidates (let’s say, infinite) with an equal repartition between men and women, the events (meeting a candidate of one specific gender) are independent. Each time you meet a candidate, you have a 50% chance that the candidate is male or female. As a consequence, the fact to have met 6 female candidates in the morning does not impact the gender of the candidates in the afternoon. All possibilities thus have an equal probability to occur. Yet, we often think that if something happens more frequently than normal during some period, then it will happen less frequently in the future.
In situations where what is being observed is random, like here, this belief is false. This is the gambler’s fallacy (or hot hand fallacy). It results from the tendency of heuristics to build coherent stories from independent random events. I failed my exam today…this is because I saw a black cat in the morning, right?
Frederick, S. (2005). Cognitive reflection and decision making. The Journal of Economic Perspectives, 19(4), 25-42.
Photo by: Jam Adams