document.write( "Question 1198614: ii. If P(B)=0.30, P(A│B)=0.60, P(B’)=0.70 and P(A│B’)=0.50, find P(B│A). \n" ); document.write( "

Algebra.Com's Answer #832269 by ikleyn(52795) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "If P(B)=0.30, P(A│B)=0.60, P(B’)=0.70 and P(A│B’)=0.50, find P(B│A).
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " The condition P(B') = 0.7 is excessive in formulation of this problem.\r
\n" ); document.write( "\n" ); document.write( " It follows automatically from the given condition P(B) = 0.30.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "From  P(B)=0.30  and  P(A│B)=0.60,  we find  P(A ∩ B)  = 0.30*0.60 = 0.18.\r\n" );
document.write( "\r\n" );
document.write( "From  P(B')=0.7  and  P(A│B')=0.5,  we find  P(A ∩ B') = 0.50*0.70 = 0.35.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From  P(A ∩ B)  = 0.18  and  P(A ∩ B') = 0.35  we find\r\n" );
document.write( "\r\n" );
document.write( "      P(A) = P(A ∩ B) + P(A ∩ B') = 0.18 + 0.35 = 0.53.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From  P(A ∩ B) = 0.18  and  P(A) = 0.53  we find\r\n" );
document.write( "\r\n" );
document.write( "      P(B|A) = P(A ∩ B) / P(A) =  =  = 0.3396  (rounded).    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );