document.write( "Question 581758: a computer program consists of two blocks written independently by two different programmers. the first block has an error with probability .2. the second block has an error with probability .3. if the program returns an error, what is probability that there is an error in both blocks? \n" ); document.write( "

Algebra.Com's Answer #815969 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "The original problem, as it is posted, worded and printed, creates many questions to its content.\r
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document.write( "    There is a universal finite set U and two its subsets A and B.\r\n" );
document.write( "    The experiment is to select randomly some element from the universal set U.\r\n" );
document.write( "    The probability to select randomly any element from U is the same for all elements of U.\r\n" );
document.write( "    With probability 0.3, the selected element is from subset A; with probability 0.2, the selected element is from subset B.\r\n" );
document.write( "    The selection is independent between subsets A and B.\r\n" );
document.write( "    If an element is selected from the union (A U B), what is the probability that it is from the intersection (A ∩ B) ?\r\n" );
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\n" ); document.write( "\n" ); document.write( " SOLUTION\r
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document.write( "The problem asks about the conditional probability  P = P (A ∩ B) / P(A U B).\r\n" );
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document.write( "Due to the independence,  P(A ∩ B) = P(A)*P(B) = 0.3*0.2 = 0.06.\r\n" );
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document.write( "From the general Probability Theory formula,  P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.3 + 0.2 - 0.06 = 0.44.\r\n" );
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document.write( "THEREFORE, the final conditional probability under the problem's question is  P =  = 0.136364  (rounded).    ANSWER\r\n" );
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