document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119128>Question 1119128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fair die is tossed. Consider events A = {2, 4, 6}, B = {1, 2}, C = {1, 2, 3, 4}. Find:<BR>\n" );
document.write( "1. P(A and B) and P(A or C)<BR>\n" );
document.write( "2. P(A|B) and P(B|A) <BR>\n" );
document.write( "3. P(A|C) and P(C|A)<BR>\n" );
document.write( "4. P(B|C) and P(C|B) </SPAN>\n" );
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document.write( "Given A = {2, 4, 6}, B = {1, 2}, C = {1, 2, 3, 4}, we can find<br><BR>\n" );
document.write( "(A and B) = {2}  (all the elements in BOTH A AND B); (A or C) = {1, 2, 3, 4, 6}.  (all the elements in EITHER A OR C)<br><BR>\n" );
document.write( "Question (1):  So then P(A and B) = 1/6; P(A or C) = 5/6.<br><BR>\n" );
document.write( "For the conditional probability problems like P(A|B), I find it easiest to view the problem as B being the sample space, and the \"good\" elements are the elements of B that are also elements of A.  So...<br><BR>\n" );
document.write( "P(A|B):  B contains two elements, 1 and 2.  Of those, one (2) is also in A.  So P(A|B) is 1/2.<br><BR>\n" );
document.write( "P(B|A):  A contains three elements, 2, 4, and 6.  Of those, one (2) is also in B.  So P(B|A) is 1/3.<br><BR>\n" );
document.write( "You can answer the others in a similar manner.  Here are the types of questions you need to ask:<br><BR>\n" );
document.write( "P(A|C):  What fraction of the elements of C are also elements of A?<BR>\n" );
document.write( "P(C|A):  What fraction of the elements of A are also elements of C?<br><BR>\n" );
document.write( "and likewise for P(B|C) and P(C|B). </SPAN>\n" );
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