Question

1-Assuming events are independent when they are not- The likelihood of two independent events both happening is the product of their individual probability.So if we assume the events to be independent when they are actually not, pose problems and results in wrong interpretations of the overall probability for the overall event.

2- Not understanding when events are NOT independent- A different kind of mistake occurs when events that are not independent treated as such.As The likelihood of two independent events, both happening is the product of their individual probability but if the occurrence of second event dependent on the occurrence of first, then the probability of the overall event is different.So it is important to understand when events are NOT independent.

3- Cluster happen- In this the larger the size better is the happening of an event. For e.g Consider a class of 100 students and everyone is asked to flip a coin and anyone who flips head must sit down.Assuming we start with 100 students, roughly 50 will sit down after the first flip.Then we do it again.after which 25 or so are still standing and so on.More often than not there will be a student standing at the end who as flipped 5 or 6 tails in a row.When we see an anomalous event like that out of context, we assume that something besides randomness must be responsible

4-The prosecutor’s fallacy - A general term for an invalid interpretation of a valid statistic.The prosecutor's fallacy occurs when the context surrounding statistical evidence is neglected.

5-Reversion to the mean (or regression to the mean)-The tendency for extreme sets of results to become more average as the set grows. Neglecting regression toward the mean is a common error of statistical analysis.

6-Statistical discrimination-It is an economic theory of racial or gender inequality based on stereotypes. According to this theory, inequality may exist and persist between demographic groups even when economic agents (consumers, workers, employers, etc.) are rational and non-prejudiced.

Pick one of these and give an example

Answer 1

6. STATISTICAL DISCRIMINATION -

The theory posits that in the absence of direct information about a certain fact of ability, a decision maker would substitute group averages. For instance, labor market discrimination may exist because employers don't know with certainty workers' ability, therefore they may resort to basing employment decisions on the workers' visible features, such as group identity, as long as these features correlate with some desirable but more difficult to measure trait. The result is that atypical individuals from the disadvantaged group suffer unfair discrimination.

Statistical discrimination is often used  for example  when older people are charged more for life insurance, or when a college diploma is required for a job (because it is believed that college graduates perform, on average, better).