document.write( "Question 1187913: Events A and B are independent, P(A)=0.49 and P(A∪B)=0.83.\r
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Algebra.Com's Answer #818930 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "Events A and B are independent, P(A)=0.49 and P(A∪B)=0.83.
\n" ); document.write( "Find P(A∩B) as a decimal or fraction.
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document.write( "Since Events A and B are independent, we can express  P(A∩B) as\r\n" );
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document.write( "    P(A∩B) = P(A)*P(B) = 0.49*P(B).      (1)\r\n" );
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document.write( "Next, we use the general formula for P(AUB)\r\n" );
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document.write( "    P(AUB) = P(A) + P(B) - P(A∩B).\r\n" );
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document.write( "We substitute here  P(AUB) = 0.83 (given);  P(A) = 0.49 (given)  and P(A∩B) = 0.49*P(B)  from (1).\r\n" );
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document.write( "We get then\r\n" );
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document.write( "    0.83 = 0.49 + P(B) - 0.49*P(B),\r\n" );
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document.write( "which gives\r\n" );
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document.write( "    0.83 - 0.49 = P(B)*(1-0.49),\r\n" );
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document.write( "        0.34    = 0.51*P(B)\r\n" );
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document.write( "        P(B) =  = .\r\n" );
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document.write( "Now from (1),  finally,   P(A∩B) = 0.49*P(B) =  =  = 0.32666666...   ANSWER\r\n" );
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