200 students took part in a survey. To the question "Are you taking History?", 80 replied yes. To the question "Are you taking Math?", 90 replied yes. To the question "Are you taking Math and History?", 20 replied yes. How many students are taking neither Math nor Historv? (Enter vour answer as a single integer)
200 students took part in a survey. To the question "Are you taking History?", 80 replied yes. To the question "Are you taking Math?", 90 replied yes. To the question "Are you taking Math and History?", 20 replied yes. How many students are taking neither Math nor Historv? (Enter vour answer as a single integer)
COMPREHENSIVE MICROSOFT OFFICE 365 EXCE
1st Edition
ISBN:9780357392676
Author:FREUND, Steven
Publisher:FREUND, Steven
Chapter3: Working With Large Worksheets, Charting, And What-if Analysis
Section: Chapter Questions
Problem 2.3EYK
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Question
200 students took part in a survey.
To the question "Are you taking History?", 80 replied yes.
To the question "Are you taking Math?", 90 replied yes.
To the question "Are you taking Math and History?", 20 replied yes.
How many students are taking neither Math nor Historv?
(Enter vour answer as a single integer)
Expert Solution
Step 1
We can use the principle of inclusion-exclusion to find the number of students who are not taking either Math or History.
Let M be the set of students taking Math, and H be the set of students taking History. Then we want to find the size of the set M ∪ H^c, where H^c is the complement of H (i.e., the set of students not taking History).
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