document.write( "Question 1206354: Give that A and B are independent and P(A)=1/5 and P(AUB)=1/4. Find P(A') and P(B) \n" ); document.write( "

Algebra.Com's Answer #843748 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Given that A and B are independent and P(A)=1/5 and P(AUB)=1/4. Find
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document.write( "(a)  P(A') = 1 - P(A) = 1 - 1/5 = 4/5.     (A' is the complement to B).\r\n" );
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document.write( "(b)  Use the general formula, which is always valid\r\n" );
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document.write( "         P(A U B) = P(A) + P(B) - P(A and B).    (1)\r\n" );
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document.write( "     Since A and B are independent, we have P(A and B) = P(A)*P(B) = .\r\n" );
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document.write( "     Substituting the values into formula (1), we get\r\n" );
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document.write( "          =  + P(B) - .\r\n" );
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document.write( "      Multiply both sides by 20\r\n" );
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document.write( "         5 = 4 + 20*P(B) - 4*P(B)\r\n" );
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document.write( "         5 - 4 = 16*P(B)\r\n" );
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document.write( "           1   = 16*P(B)\r\n" );
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document.write( "           P(B) = .   ANSWER\r\n" );
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