document.write( "Question 892252: Two students are registered for the same class and attend independently of each other, student A 70% of the time and student B 60% of the time. The teacher remembers that on a given day at least one of them is in class. What is the probability that student A was in class that day? \n" ); document.write( "

Algebra.Com's Answer #540396 by Edwin McCravy(20056) $\"\"$ $\"About$

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Two students are registered for the same class and attend independently of each
\n" ); document.write( "other, student A 70% of the time and student B 60% of the time. The teacher
\n" ); document.write( "remembers that on a given day at least one of them is in class. What is the
\n" ); document.write( "probability that student A was in class that day?
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document.write( "This is conditional probability.  The probability that A was in class, given\r\n" );
document.write( "that A or B was in class that day.\r\n" );
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document.write( "The formula is\r\n" );
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document.write( "          P(X and Y) \r\n" );
document.write( "P(X|Y) = ------------\r\n" );
document.write( "            P(Y)\r\n" );
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document.write( "where X = A,  Y = (A or B)\r\n" );
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document.write( "              P(A and (A or B))     P(A)\r\n" );
document.write( "P(A|A or B) = ----------------- = ---------\r\n" );
document.write( "                  P(A or B)       P(A or B)\r\n" );
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document.write( "We know P(A) = .70.  We need P(A or B) \r\n" );
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document.write( "The complement of 'at least 1' is 'none at all'.\r\n" );
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document.write( "student A attends 70% of the time.\r\n" );
document.write( "Therefore A is absent 30% of the time.  Probability .3\r\n" );
document.write( "Student B attends 60% of the time. Probability .6 \r\n" );
document.write( "Therefore B is absent 40% of the time. Probability .4\r\n" );
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document.write( "They are both absent (.3)(.6) = .18 or 18% of the time.\r\n" );
document.write( "So 1 or the other is present 82% of the time.  Probability =.82.\r\n" );
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document.write( "              P(A and (A or B))     P(A)        .3      30     15\r\n" );
document.write( "P(A|A or B) = ----------------- = --------- = ------ = ---- = ----\r\n" );
document.write( "                  P(A or B)       P(A or B)    .82      82     41\r\n" );
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document.write( "Probability about .366 or 36.6%of the time.\r\n" );
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document.write( "Edwin

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