Theoretical Probability: A Real-Life Example (from Digital Design)

Calculating theoretical probability is a common practice in the design of digital products, like apps and websites. This blog post showcases a specific example of how music streaming websites utilize theoretical probability to recommend songs to their listeners.

Theoretical Probability in Digital Product Design (UX Design)


When creating apps, websites, or digital products, it’s crucial to consider how users will interact with them—how easy and convenient they’ll be to use. This task often falls on UX designers (User eXperience). In their work, UX designers sometimes need to calculate theoretical probability. Let’s explore an example of how UX design functions in the realm of music streaming services.

Music Streaming Services

Have you ever used music streaming services like Spotify or Apple Music? If you have, you’ve likely observed that these services recommend songs for you to listen to. These personalized recommendations are crafted based on your listening habits, the time of day, and various other factors. The next paragraph dives into this with a specific example and calculation.

Example of Calculating Theoretical Probability:

Imagine a music streaming service with a whopping 100,000 songs in its database, and the user has listened to 20 of them. Initially, the service could randomly recommend any song from this extensive collection. However, the theoretical probability that the user will enjoy a randomly selected song is quite low:

\[ \frac{20}{100,000} \times 100\% = 0.02\% \]

This probability may seem tiny, but there’s a way to enhance it.

Let’s say, out of those 20 songs, 15 belong to the “psychedelic folk” genre. Additionally, suppose the service has 5,000 more songs in its database falling under the “psychedelic folk” category.

The theoretical probability that the user will enjoy a randomly selected “psychedelic folk” song becomes:

\[ \frac{15}{5,000} \times 100\% = 0.3\% \]


While this probability is still relatively small, it’s 15 times larger than the initial probability! By incorporating additional parameters like genre and tempo, music streaming services, as well as other apps or websites, can significantly boost the theoretical probability of providing relevant recommendations. This enhancement is commonly referred to as recommendation accuracy.


Understanding and calculating theoretical probability play crucial roles in real-world scenarios you encounter daily. It’s worth noting that the intricate calculations involved, especially in large music streaming companies, are typically undertaken by scientists and researchers dedicated to improving the theoretical probability of accurate recommendations. Nevertheless, collaboration between these specialists and UX designers is common, emphasizing the importance for a UX designer to possess a general understanding of how theoretical probability calculations work.


This simplified example is based on insights from various scientific publications, including one co-authored by individuals from Spotify:

While the full publication may be challenging, you’re encouraged to explore Chapter 1 “Introduction” and examine some figures (e.g., Figure 1 and Figure 2) to grasp the fundamental role of math and probability in Spotify’s recommendations.

Additionally, for a broader understanding of the importance of math in digital and UX design, you can read a general article that emphasizes the significance of probability and statistics.

Video Version

Our animated video further explains how to enhance the theoretical probability of accurate song recommendations, featuring examples of David Bowie songs. Enjoy the preview below or subscribe for access to our full videos.

Further Reading

Calculating theoretical probability proves valuable in various domains. Check out another example of ours that explains its application in Artificial Intelligence:

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