document.write( "Question 1137147: If P(B)equals 0.2, P(A | B)equals 0.5, P(Upper B prime)equals 0.8, and P(A | Upper B prime)equals 0.7, find P(B | A). \n" ); document.write( "

Algebra.Com's Answer #754970 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "Given info:
\n" ); document.write( "P(B) = 0.2
\n" ); document.write( "P(A|B) = 0.5
\n" ); document.write( "P(B') = 0.8
\n" ); document.write( "P(A|B') = 0.7\r
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\n" ); document.write( "\n" ); document.write( "Through the law of total probability, we can say,
\n" ); document.write( "P(A) = P(A|B)*P(B) + P(A|B')*P(B')
\n" ); document.write( "P(A) = 0.5*0.2 + 0.7*0.8
\n" ); document.write( "P(A) = 0.66\r
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\n" ); document.write( "\n" ); document.write( "Now use Bayes Theorem to get the conditional probability we want
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\n" ); document.write( "\n" ); document.write( "The approximate answer, accurate to four decimal places, is 0.1515
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