SOLUTION: A group of eleven people can speak either English or French or both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can sp

2 ways, by formula or Venn diagram and a system of equations:

 P(E or F) = P(E) + P(F) - P(E and F)

         1 = 7/11 + 6/11 - P(E and F)

         1 = 13/11 - P(E and F)

P(E and F) = 13/11 - 1

P(E and F) = 13/11 - 11/11

P(E and F) = 2/11 

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You can also do it by Venn diagram and a system of equations:





Solve that system and get

a=5, b=2, c=4

5 speak English only, 2 speak both, 4 speak French only

Thus, the desired probability is 2 out of 11, or 2/11.

Edwin