Question 1088665
<pre>
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:

{{{drawing(300,200,-4,4,-2,4.8, locate(-2,1.8,a),locate(1.5,1.7,c), locate(-3.6,2.5,E), locate(-.1,1.8,b),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,F)
 )}}}

{{{system(a+b+c=11,a+b=7,b+c=6)}}}

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</pre>