document.write( "Question 1170103: A and B are the two events in S, and P(A)=0.9 and P(B)=0.6\r
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Algebra.Com's Answer #795003 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "We have  \r\n" );
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document.write( "    P(A U B) = P(A) + P(B) - P(A ∩ B) <= 1.\r\n" );
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document.write( "Hence,\r\n" );
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document.write( "    P(A ∩ B) >= P(A) + P(B) - 1 = 0.9 + 0.6 - 1 = 1.5 - 1 = 0.5.\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "(a)  It is not possible that P(A ∩ B) = 0.1  (see above)\r\n" );
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document.write( "(b)  Smallest possible value for P(A ∩ B)  is  0.5 in this case\r\n" );
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document.write( "          (and  max(0, P(A)+P(B)-1)  in general case).\r\n" );
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