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Cardinality of Sets

In a combined...

Question

In a combined test in English and Physics; 36% candidates failed in English; 28% failed in Physics and 12% in both; find the percentage of passed candidates.

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Solution

Total percentage of candidates which failed can be found using the formula of union of sets
$n (A U B) = n (A) + n (B) - n (C)$
So, $n (A U B) = 36 + 28 - 12 = 52$
Since $52$ % of the total candidates failed , percentage of passed candidates $= 100 - 52 = 48$ %

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