Among employees of a certain firm, 80% know Java, 30% know Python, and 20% know both. What proportion of programmers do not know Python? 0.90 0.80 0.14 0.70 0.20
The correct answer and explanation is:
To solve this problem, we need to find the proportion of employees who do not know Python.
Step 1: Understand the given information
- 80% know Java
- 30% know Python
- 20% know both Java and Python
We need to determine how many employees do not know Python. This involves finding the complement of the percentage of employees who know Python.
Step 2: Break down the groups
- Employees who know both Java and Python = 20% (this group is already included in the 80% who know Java and the 30% who know Python)
- Employees who know only Python = Total Python knowledge minus those who know both:
30% – 20% = 10% - Employees who know only Java = Total Java knowledge minus those who know both:
80% – 20% = 60%
Step 3: Determine the proportion of employees who do not know Python
The total percentage of employees who know Python is 30%, which includes those who know both Java and Python (20%) and those who know only Python (10%).
Therefore, the proportion of employees who do not know Python is the complement of those who know Python.
This can be calculated as: 1−Proportion who know Python=1−0.30=0.701 – \text{Proportion who know Python} = 1 – 0.30 = 0.70
Step 4: Conclusion
The correct answer is 0.70, meaning 70% of employees do not know Python.
Final Answer:
The proportion of employees who do not know Python is 0.70.