document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119951>Question 1119951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this in simple way. Thank You.\r<BR>\n" );
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document.write( "Determine all joint probabilities listed below from the following information:\r<BR>\n" );
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document.write( "P(A)=0.73,P(Ac)=0.27,P(B|A)=0.56,P(B|Ac)=0.69\r<BR>\n" );
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document.write( "P(A and B) =  \r<BR>\n" );
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document.write( "P(A and Bc) =  \r<BR>\n" );
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document.write( "P(Ac and B) =  \r<BR>\n" );
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document.write( "P(Ac and Bc)  </SPAN>\n" );
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document.write( "By definition, P(B|A) = (P(A and B))/(P(A))<br><BR>\n" );
document.write( "Think of the conditional probability as having only A as the sample space (so P(A) is the denominator of the probability fraction); you want to know what percentage of A is also B.<br><BR>\n" );
document.write( "So for the first question,<br><BR>\n" );
document.write( "P(A and B) = (P(A))*(P(B|A)) = .73*.56 = .4088.<br><BR>\n" );
document.write( "For the second question,<br><BR>\n" );
document.write( "P(A and not B) = P(A) - P(A and B) = .73 - .4088 = .3212.<br><BR>\n" );
document.write( "For the third question, again we have, by definition,<br><BR>\n" );
document.write( "P(B| not A) = (P(B and not A))/(P(not A)), so<br><BR>\n" );
document.write( "P(B and not A) = (P(B| not A))*(P(not A)) = .69*.27 = .1863.<br><BR>\n" );
document.write( "For the fourth question, P(not A and not B) is \"all that is left\":<br><BR>\n" );
document.write( "1 - (.4088+.3212+.1863) = .0837. </SPAN>\n" );
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