document.write( "Question 1206319: A sample is selected from one of two populations,
\n" ); document.write( "S1 and S2,
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\n" ); document.write( "P(S1) = 0.7
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\n" ); document.write( "P(S2) = 0.3.
\n" ); document.write( " The probabilities that an event A occurs, given that event
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\n" ); document.write( "P(A|S1) = 0.2
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\n" ); document.write( "P(A|S2) = 0.1.
\n" ); document.write( "Use the Law of Total Probability to find P(A). \n" ); document.write( "

Algebra.Com's Answer #843684 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "I am quite sure that this student's instructor's standard notation\r\n" );
document.write( "is for the subscripted S's, S1, ... Sn to form a partition of set A,\r\n" );
document.write( "where all S's are mutually disjoint and their union is A.\r\n" );
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document.write( "So I don't think it necessary that the student state that the S's are\r\n" );
document.write( "mutually disjoint nor than their union is the set A.  However, this \r\n" );
document.write( "student must know this to use the law of total probability. \r\n" );
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document.write( "The Law of Total Probability states:\r\n" );
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document.write( "Given a partition of A, that is, n mutually disjoint sets \r\n" );
document.write( "S1, S2, ... Sn\r\n" );
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document.write( "such that S1 U S2 U ... U Sn = A, \r\n" );
document.write( "then  \r\n" );
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document.write( "P(A) = P(A ∩ S1) + P(A ∩ S2) + ... + P(A ∩ Sn) =\r\n" );
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document.write( "P(A|S1)P(S1) + P(A|S2)P(S2) + ... + P(A|Sn)P(Sn)  \r\n" );
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document.write( "Here n=2\r\n" );
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document.write( "Edwin

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