In a group of 15 people; 7 can read French, 8 can read English

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In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is

  1. 10
  2. 9
  3. 5
  4. 4

Answer

Number of people who can read French, n(F) = 7

Number of people who can read English, n(E) = 8

Number of people who can read English or French of both is

n(E ∪ F) = 15 - 3 = 12

Number of people who can read both English and French,

n(E ∩ F) = n(F) + n(E) - n(E ∪ F)

n(E ∩ F) = 7 + 8 - 12 = 3

Number of people who can read exactly one language = 12 - 3 = 9

By Venn Diagram:

The correct option is B.