document.write( "Question 1172475: Given P(A) = 0.74 , P(B) = 0.25 , and P(A ∩B) = 0.13. Calculate \r
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Algebra.Com's Answer #797518 by ikleyn(52915) $\"\"$ $\"About$

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\n" ); document.write( "Given P(A) = 0.74 , P(B) = 0.25 , and P(A ∩B) = 0.13. Calculate
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document.write( "(1)  It is easy.\r\n" );
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document.write( "     Use the basic general formula of elementary probability theory\r\n" );
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document.write( "             P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.74 + 0.25 - 0.13 = 0.86.    ANSWER\r\n" );
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document.write( "(2)  To calculate P(A ∩ B’), ask yourself what is the set (A ∩ B’) ?\r\n" );
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document.write( "     This set are those elements of A that do not belong to B.\r\n" );
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document.write( "     In other words,  (A ∩ B’) = A \ (A ∩ B), where the sign  \" \ \" means subtracting the set (A ∩ B) from A.\r\n" );
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document.write( "     After this notice, it is OBVIOUS that  P(A ∩ B’) = P(A) - P(A ∩ B) = 0.74 - 0.13 = 0.61.    ANSWER\r\n" );
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document.write( "(3)  P(A'|B')  is the conditional probability  P(A' ∩ B’) / P(B').\r\n" );
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document.write( "     To calculate P(A' ∩ B’), ask yourself what is the set (A' ∩ B’) ?\r\n" );
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document.write( "     It is the set of elements that do not belong NEITHER A NOR B.\r\n" );
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document.write( "     In other words, it is the COMPLEMENT of the set (A U B) to the universal set.\r\n" );
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document.write( "     THEREFORE, P(A' ∩ B’) = 1 - P(A U B) = 1 - 0.86 = 0.14,\r\n" );
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document.write( "                             as we just defined the value of P(A U B) = 0.86  in n.(1) above.\r\n" );
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document.write( "     After this notice, it is OBVIOUS that  P(A'|B') = P(A' ∩ B’) / P(B') =  =  =  = 0.186667 (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see other similar solved problems, look into the lesson\r
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