School board officials are debating whether to require all high school seniors to take a proficiency exam before graduating. A student passing all three parts (mathematics, language skills, and general knowledge) would be awarded a diploma; otherwise, he or she would receive only a certificate of attendance. A practice test given to this year€™s ninety-five hundred seniors resulted in the following numbers of failures:

If €œStudent fails mathematics,€ €œStudent fails language skills,€ and €œStudent fails general knowledge€ are independent events, what proportion of next year€™s seniors can be expected to fail to qualify for a diploma? Does independence seem a reasonable assumption in this situation?

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Subject Area Number of Students Failing Mathematics Language skills General knowledge 3325 1900 1425