Proportion of Programmers who Know Java or Python

What proportion of programmers know neither Java nor Python?

Among employees of a certain firm, 70% know Java, 60% know Python, and 50% know both.

Answer:

By using set theory and Venn diagrams, we find that 20% of the employees know neither Java nor Python when accounting for the overlap of those who know both.

Explanation: To solve this problem, we can use principles of set theory and Venn diagrams. We know that 70% of employees know Java and 60% know Python, with an overlap where 50% know both. This overlap must be subtracted from the total percentages of Java and Python to avoid double counting those who know both languages.

When we subtract the 50% who know both from the total percentage who know Java and Python separately, we get:

Java only: 70% - 50% = 20%

Python only: 60% - 50% = 10%

Adding the proportions of employees who know Java only, Python only, and both Java and Python: (Java only) 20% + (Python only) 10% + (Both) 50% = 80%

This means that 80% of the employees know either Java or Python or both. To find the proportion that knows neither Java nor Python, we subtract this from the total 100%:

100% - 80% = 20%

Therefore, 20% of the employees know neither Java nor Python.