00 children took three examinations. 40 passed the first, 39 passed the second and 48 passed the third, 19 passed all three, 9 passed first two and failed in third 19 failed in the first two and passed the third. Find how many children passed at least two examinations. Show that for the question asked certain of the given frequencies are not necessary.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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100 children took three examinations. 40 passed the first, 39 passed the second and 48 passed the third, 19 passed all three, 9 passed first two and failed in third 19 failed in the first two and passed the third. Find how many children passed at least two examinations. Show that for the question asked certain of the given frequencies are not necessary.

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