Question

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

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 $straight P left parenthesis straight A union straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A intersection straight B right parenthesis$
$rightwards double arrow space space space space space space space space space space space space space space space space space space space 7 over 11 space equals space 6 over 11 plus 5 over 11 minus space straight P left parenthesis straight A space intersection space straight B right parenthesis rightwards double arrow space space space space space space space space space space space space space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 6 over 11 plus 5 over 11 minus 7 over 11 space equals space fraction numerator 6 plus 5 minus 7 over denominator 11 end fraction space equals 4 over 11$

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