document.write( "Question 1203256: The probability that an event A occurs is P(A) = 0.4. B is an event independent of A and P(A U B) = 0.7. Find P (B). \n" ); document.write( "

Algebra.Com's Answer #838677 by ikleyn(52793) $\"\"$ $\"About$

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\n" ); document.write( "The probability that an event A occurs is P(A) = 0.4.
\n" ); document.write( "B is an event independent of A and P(A U B) = 0.7. Find P (B).
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document.write( "Start from general formulas\r\n" );
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document.write( "    P(A U B) = P(A) + P(B) - P(A n B),  P(A n B) = P(A)*(P(B).\r\n" );
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document.write( "Substitute the given data there.  You will get\r\n" );
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document.write( "   0.7 = 0.4 + P(B) - 0.4*P(B).\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "    0.7 - 0.4 = P(B) - 0.4*P(B),\r\n" );
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document.write( "    0.3 = 0.6*P(B)\r\n" );
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document.write( "    P(B) =  = 0.5.\r\n" );
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document.write( "ANSWER.  P(B) = 0.5.\r\n" );
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