Probability in Action

We are living in a world where "events" happen all the time and we cannot always predict all the outcomes of the events accurately. However, with probability and statistics, we can predict their outcomes based on the acquired data of the events.

Probability and statistics are used widely, not only in modern industries but also other fields such as military, weather, sports, etc.

Risk management is one thing that is quite important to be taken into consideration for planning, operation and management of systems.

I learned many things this week in the SYSE 515 class. One thing that I particularly liked was Bayes' Theorem.

Unlike independent events such as flipping coins or rolling a dice, calculating conditional probabilities can sound more tricky since it can seem as if there is not enough information to solve the problem. Bayes' Theorem is applied here to find out conditional probabilities.

Here is an example question from the following website.

https://www.investopedia.com/terms/b/bayes-theorem.asp

As a numerical example, imagine there is a drug test that is 98% accurate, meaning 98% of the time it shows a true positive result for someone using the drug and 98% of the time it shows a true negative result for nonusers of the drug. Next, assume 0.5% of people use the drug. If a person selected at random tests positive for the drug, the following calculation can be made to see whether the person is actually a user of the drug.

The question can be translated into

P(the person is actually a user of the drug|tests positive for the drug)=

P(tests positive for the drug|the person is actually a user of the drug)*P(the person is actually a user of the drug)/P(tests positive for the drug)

which is 

(0.98*0.005)/[(0.98*0.005)+{(1-0.98)*(1-0.005)}]=19.76%

The number shows that it is much more like the person is not a user of the drug even if the test result was positive.

Likewise, one of the exercise questions that my team chose from the textbook could be solved using the Bayes' Theorem.

References:

Risk Management - Standard Process/Definitions: Probability of Occurence. (n.d.). RISK MANAGEMENT TOOLKIT. Retrieved August 23, 2020, from http://www2.mitre.org/work/sepo/toolkits/risk/StandardProcess/definitions/occurence.html

Bayes’ Theorem. (2003, September 30). Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/bayes-theorem/

Sarkar, T. (n.d.). Bayes’ rule with a simple and practical example - Towards Data Science. Medium. Retrieved August 23, 2020, from https://towardsdatascience.com/bayes-rule-with-a-simple-and-practical-example-2bce3d0f4ad0

Hayes, A. (2020, June 14). Bayes’ Theorem. Investopedia. https://www.investopedia.com/terms/b/bayes-theorem.asp