Fraction of a team who know both Python and R

Question

On a data team, 70\% of members know Python, 50\% know R, and 90\% know at least one of the two languages. What fraction of the team know both Python and R?

Accepted Answer

The union is given (90\% know at least one), and we want the overlap. Rearranging inclusion-exclusion, P(	ext{both}) = P(	ext{Python}) + P(	ext{R}) - P(	ext{either}) = 0.70 + 0.50 - 0.90 = 0.30. So 30\% know both. Checking the split: Python only 0.40, R only 0.20, both 0.30, neither 0.10, which sum to 1.00. Takeaway. To recover a hidden overlap, subtract the union from the sum of the individual shares.

Fraction of a team who know both Python and R

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