If $straight P left parenthesis straight A right parenthesis space equals space 6 over 11 comma space space space straight P left parenthesis straight B right parenthesis space equals space 5 over 11 space space and space straight P left parenthesis straight A space union space straight B right parenthesis space equals space 7 over 11 comma space space find space straight P left parenthesis straight B space left enclose straight A right parenthesis$ .

Solution

Here $straight P left parenthesis straight A right parenthesis space equals space 6 over 11 comma space space straight P left parenthesis straight B right parenthesis space equals space 5 over 11 comma space space straight P left parenthesis straight A union straight B right parenthesis space equals space 7 over 11$
Now, $straight P left parenthesis straight B space left enclose straight A right parenthesis end enclose space space equals space fraction numerator straight P left parenthesis straight B intersection straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space equals fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space equals fraction numerator begin display style 4 over 11 end style over denominator begin display style 6 over 11 end style end fraction space equals space 4 over 6 space equals space 2 over 3$

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