document.write( "Question 1142346: p(A)=0.50,P(A/B)=O.50,P(B)=0.80.
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Algebra.Com's Answer #763075 by ikleyn(52906) $\"\"$ $\"About$

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document.write( "By the definition,  P(A|B) = P(A & B)/P(B);\r\n" );
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document.write( "so, from the given data  \r\n" );
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document.write( "    P(A|B) = P(A & B)/P(B) = 0.50,\r\n" );
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document.write( "which gives  \r\n" );
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document.write( "    P(A & B) = 0.5*P(B) = 0.5*0.80 = 0.4.\r\n" );
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document.write( "Thus P(A intersection B) is just found:  it is  P(A intersection B) = P(A & B) = 0.4.\r\n" );
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document.write( "If  P(A & B) = 0.4,  then\r\n" );
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document.write( "    P(A U B) = P(A) + P(B) - P(A & B) = 0.5 + 0.8 - 0.4 = 0.9.\r\n" );
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document.write( "The last question is\r\n" );
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document.write( "        are A and B independent ?\r\n" );
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document.write( "Two events X and Y are called independent if P(X & Y) = P(X) * P(Y).\r\n" );
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document.write( "Lets check if it is valid for our A and B.\r\n" );
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document.write( "We just found that  P(A & B) = 0.4;  but  P(A)*P(B) = 0.5*0.4 = 0.2  has DIFFERENT value.\r\n" );
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document.write( "ANSWER.  P(A & B) = 0.4;  P(A U B) = 0.9;  \r\n" );
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document.write( "         the events A and B are NOT independent.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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