document.write( "Question 1203674: Let P(A) = 0.4 and P(A u B) 0.6:
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Algebra.Com's Answer #839448 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "Let P(A) = 0.4 and P(A u B) = 0.6:
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document.write( "          Part (a) solution\r\n" );
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document.write( "Events A and B are mutually exclusive if and only if  P(A U B) = P(A) + P(B).\r\n" );
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document.write( "In our case, it should be\r\n" );
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document.write( "         0.6 = 0.4 + P(B),\r\n" );
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document.write( "which gives  P(B) = 0.6 - 0.4 = 0.2.\r\n" );
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document.write( "ANSWER.  P(B) = 0.2.\r\n" );
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document.write( "          Part (b) solution\r\n" );
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document.write( "We have a general formula P(A U B) = P(A) + P(B) - P(A n B), which is valid for all events A and B.\r\n" );
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document.write( "If A and B are independent, then  P(A n B) = P(A)*P(B).\r\n" );
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document.write( "So, in our case should be\r\n" );
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document.write( "    0.6 = 0.4 + P(B) - 0.4*P(B),\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    0.6 - 0.4 = 0.6*P(B)\r\n" );
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document.write( "       0.2    = 0.6*P(B)\r\n" );
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document.write( "       P(B) =  = .\r\n" );
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document.write( "ANSWER.  P(B) should be .\r\n" );
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