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Least proportion passing every subject

Least proportion passing every subject

IP 4
8 marks
  1. For any two events \(A\) and \(B\), show that \(\mathrm{P}(A\cap B)\ge \mathrm{P}(A)+\mathrm{P}(B)-1\).[2]
  2. In a cohort, \(85\%\) of the students passed Mathematics and \(70\%\) passed Science. Use (a) to find the least possible percentage of students who passed both subjects, and explain why at most \(70\%\) passed both.[3]
  3. In addition, \(90\%\) of the cohort passed English. Show that at least \(45\%\) of the cohort passed all three subjects.[3]

Solution:

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Answer:(a) shown (b) at least \(55\%\); at most \(70\%\) because those passing both are among the \(70\%\) who passed Science (c) shown

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