Students majoring in neither English nor History

Question

At one university, $30\%$ of students study English, $45\%$ study History, and $15\%$ are double majors in both subjects. What share of the students majors in neither subject?

Short answer

$40\%$ . By inclusion–exclusion, the share majoring in at least one subject is $30+45-15=60\%$ , so $40\%$ major in neither.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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