document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182451>Question 1182451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let A and B be events with P(A)=1/2, P(B)=1/3 and P(A∩B)=1/4. Find <BR>\n" );
document.write( "i)   P(A | B)<BR>\n" );
document.write( "ii)  P(B | A)<BR>\n" );
document.write( "iii) P(A U B)<BR>\n" );
document.write( "iv)  P(A'| B') </SPAN>\n" );
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document.write( "Use 12 as the denominator for each probability, since 12 is the least common multiple of 2, 3, and 4.<br><BR>\n" );
document.write( "Given: P(A) = 6/12; P(B) = 4/12; P(A∩B) = 3/12<br><BR>\n" );
document.write( "Then<BR>\n" );
document.write( "P(A∩B') = P(A)-P(A∩B) = 6/12-3/12 = 3/12<BR>\n" );
document.write( "P(A'∩B) = P(B)-P(A∩B) = 4/12-3/12 = 1/12<br><BR>\n" );
document.write( "P(AUB) = P(A)+P(B)-P(A∩B) = 6/12+4/12-3/12 = 7/12<BR>\n" );
document.write( "P(A'∩B') = 1-P(AUB) = 1-7/12 = 5/12<br><BR>\n" );
document.write( "i) P(A|B) = P(A∩B)/P(A) = (3/12)/(6/12) = 3/6 = 1/2<br><BR>\n" );
document.write( "ii) P(B|A) = P(A∩B)/P(B) = (3/12)/(4/12) = 3/4<br><BR>\n" );
document.write( "iii) (from above) P(AUB) = 7/12<br><BR>\n" );
document.write( "iv) P(A'|B') = P(A'∩B')/P(B') = (5/12)/(1-4/12) = (5/12)/(8/12) = 5/8<br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );