If $straight P left parenthesis straight A right parenthesis space equals space 7 over 13 comma space straight P left parenthesis straight B right parenthesis space equals space 9 over 13 comma space space straight P left parenthesis straight A intersection straight B right parenthesis space equals 4 over 13 comma space evaluate space straight P left parenthesis straight A space left enclose straight B right parenthesis$ .

Solution

Here, $straight P left parenthesis straight A right parenthesis space equals 7 over 13 comma space space straight P left parenthesis straight B right parenthesis space equals space 9 over 13 comma space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 4 over 13$ ...(1)
Now, $straight P left parenthesis straight A space left enclose straight B right parenthesis space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals space fraction numerator begin display style 4 over 13 end style over denominator begin display style 9 over 13 end style end fraction space space space space space space space space space space space space space space open square brackets because space space of space space left parenthesis 1 right parenthesis close square brackets$
$equals space 4 over 13 cross times 13 over 9 space equals 4 over 9.$

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