document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970643>Question 970643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man travels to work either by car or by train. <BR>\n" );
document.write( "There is a probability of 2/3 that he travels by train on Monday. <BR>\n" );
document.write( "If he travels by train on any one day, there is a probability of 3/4 that he will travel by car on the next day. <BR>\n" );
document.write( "If he travels by car any one day ,there is a probability of 5/6 that he will travel by train the next day. <BR>\n" );
document.write( "Find the probability that he travels:<BR>\n" );
document.write( "(a) by car on Tuesday<BR>\n" );
document.write( "(b) by train on Tuesday<BR>\n" );
document.write( "(c) by car on Wednesday<BR>\n" );
document.write( "(d) by train on Wednesday .. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593603 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A man travels to work either by car or by train. <BR>\n" );
document.write( "There is a probability of 2/3 that he travels by train on Monday. <BR>\n" );
document.write( "If he travels by train on any one day, there is a probability of 3/4 that he will travel by car on the next day. <BR>\n" );
document.write( "If he travels by car any one day ,there is a probability of 5/6 that he will travel by train the next day. <BR>\n" );
document.write( "Find the probability that he travels:<BR>\n" );
document.write( "(a) by car on Tuesday<BR>\n" );
document.write( "(b) by train on Tuesday<BR>\n" );
document.write( "(c) by car on Wednesday<BR>\n" );
document.write( "(d) by train on Wednesday ..<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Properly capitalizing the text reduces the chance of errors of interpretation.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Probabilities of travelling by car (P(C)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) or train (P(T)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2%2F3=1%2F3 ALIGN=MIDDLE  ALT=\"1-2%2F3=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) on Monday.<BR>\n" );
document.write( "Probabilities of each mode of transportation based on outcome of previous day:<BR>\n" );
document.write( "- P(CT)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > => P(CC)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-3%2F4=1%2F4 ALIGN=MIDDLE  ALT=\"1-3%2F4=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- P(TC)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > => P(TT)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-5%2F6=1%2F6 ALIGN=MIDDLE  ALT=\"1-5%2F6=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Need to draw a tree diagram of all combinations for three days (Monday to Wednesday) from which conclusions may be drawn.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "Since it is a three step process, we have a three level tree-diagram with a total of 2 outcomes for Monday {C,T}, 4 outcomes for Tuesday {CC,CT,TC,TT}, and eight outcomes for Wednesday {CCC,CCT,CTC,CTT,TCC,TCT,TTC,TTT}.<BR>\n" );
document.write( "The probabilities of outcomes of each day are shown in shown in separate columns, the sum of which must equal 1 or else there is a mistake somewhere.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "The tree diagram is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=mathmate&illustration_name=970643.jpg\"><BR>\n" );
document.write( "  <BR>\n" );
document.write( "We can read off the answers from the tree diagram as follows:<BR>\n" );
document.write( "X means any outcome, T=by train, C=by car<BR>\n" );
document.write( "(a) by car on Tuesday<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28XC%29=1%2F2%2B1%2F18=10%2F18=5%2F9 ALIGN=MIDDLE  ALT=\"P%28XC%29=1%2F2%2B1%2F18=10%2F18=5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "(b) by train on Tuesday<BR>\n" );
document.write( "P(XT)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6%2B5%2F18=8%2F18=4%2F9 ALIGN=MIDDLE  ALT=\"1%2F6%2B5%2F18=8%2F18=4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "P(XT)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-P%28XC%29=1-5%2F9=4%2F9 ALIGN=MIDDLE  ALT=\"1-P%28XC%29=1-5%2F9=4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(c) by car on Wednesday<BR>\n" );
document.write( "P(XXC)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8%2B1%2F12%2B5%2F24%2B1%2F108=23%2F54 ALIGN=MIDDLE  ALT=\"1%2F8%2B1%2F12%2B5%2F24%2B1%2F108=23%2F54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(XXT)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-23%2F54=31%2F54 ALIGN=MIDDLE  ALT=\"1-23%2F54=31%2F54\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );