Probability in Real Life > Real Life Examples of the Geometric Distribution

The Geometric distribution tells us the probability of a certain number of failures to get the first success in *k* Bernoulli trials (where the only two possible outcomes are success or failure). In class, you’re often given an example with dice rolls or choosing a card from a deck; while this can come in handy if you’re a gambler, there are many more interesting real life examples of the geometric distribution.

## List of Real Life Examples of the Geometric Distribution

**The probability that the**can be modeled with a geometric probability density function [1].*i*th item on a production line is defective- In biology,
**the length of actin filaments**follow a geometric distribution [2]. Actin polymerization concerns the hydrolysis of ATP into ADP; At each time step in the process, an actin monomer may add to the filament, or fall off. - If you’re in sales, the distribution can be used to model
**how many attempts to make a sale will end in a success.** - In welding, one way to test weld strength is to load welded joints until they fracture either in the weld, or in the beam. The distribution could be used to model
**how many joints are loaded before the first beam fracture occurs**[3]. **A safety engineer studies industrial accidents in a plant**, suspecting that 40% are caused by employees not following instructions. To test the theory, accident reports are randomly selected until one is found (a “Success”) that is caused by an employee failing to follow safety procedures [4].**A polling employee wants to find out why people voted Independent**. They randomly select a person exiting a polling station, where the probability is p = .25 that a person voted independent. The distribution tells them how many people they will need to ask before finding a person who actually voted Independent.**A company wants to survey their customers to see if they received a faulty product**, and what their feelings about their experiences are. If the probability of getting a faulty product is .01, the geometric distribution could be used to find out how many customers will need to be contacted before finding a person who received a faulty product.

## References

Image: Adobe Creative Cloud (Licensed).

[1] Iyer, R. Important Discrete Distributions: Poisson, Geometric, & Modified Geometric. Retrieved November 2, 2021 from: https://courses.engr.illinois.edu/ece313/sp2017/sectionG/Lectures/lec_10.pdf

[2] Bois, J. (2018). Tutorial 3b: Probability distributions and their stories. Retrieved November 2, 2021 from: http://bois.caltech.edu/dist_stories/t3b_probability_stories.html#Geometric-distribution

[3] Chapter 3. Discrete Random Variables and Probability Distributions. Retrieved November 2, 2021 from: http://homepage.stat.uiowa.edu/~rdecook/stat2020/notes/ch3_pt4.pdf

[4] Ilowsky, B. & Dean, S. (2021). 4.5: Geometric Distribution. Retrieved November 2, 2021 from: https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(OpenStax)/04%3A_Discrete_Random_Variables/4.05%3A_Geometric_Distribution