Question

Shoppers are questions as to the acceptability of three brands A, B and C of smart phones. Of those questioned 65 found brand A acceptable, 45 found brand B accept- able and 30 found brand C acceptable. In addition, 20 found both A and B acceptable, 15 found both A and C acceptable, and 10 found both B and C acceptable. If 100 shoppers were questioned, how many found all three brands acceptable?

Answer 1

$n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)$

Putting the values we get,

$100 = 65 + 45 + 30 - 20 - 10 - 15 + n(A \cap B \cap C)$

Then, $n(A \cap B \cap C) = 5$

So 5 people found all three brands acceptable.

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