Decision Making _ Decision Involving Probability

The Assignment:The regression fallacy, which is related to illusory correlation and the Belief in the Law of Small Numbers, is the tendency to draw conclusions about the effectiveness of actions taken in response to chance phenomena. It has the following form:•A process has two outcomes, X and Y. They occur by chance.•Outcome Y happens N times in a row, or in close succession. In response to that, …•… we take some action Z.•The next time we observe the process, the outcome is not Y, but rather X.•Erroneous conclusion: Doing Z prevented Y from happening again, when Y wouldn’t have happened anyway, since X and Y occur by chance.Part IHere is a list of some observations, actions taken as a result, and the following reactions.Observation Action Reaction A college basketball team with a good record, playing in a competitive league, loses its last three season games and fails to qualify for the NCAA Tournament. The head coach is fired. The team wins its first three games of the next season. The university president is praised for getting a new head coach. Inexplicably, three Air Force aircraft are involved in major accidents in a single 90-day period. The aircraft belong to different commands. The Air Force Chief of Staff orders an operational stand down for a service-wide training day. There are no accidents in the 90 days following the training day. The Chief thinks he’s a genius. Heather is plagued by migraines. Whenever Heather gets a migraine, she takes Tylenol, and it goes away. Heather concludes that Tylenol is effective against migraine. She orders a case of bottles from Amazon. Pick one of the above. What additional information would you need, to determine whether the regression fallacy has occurred? Alternatively; what information would you have needed before taking the action, to make sure that you’re not falling victim to the regression fallacy?