document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139000>Question 139000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> every 15 min. the fast train arrives & waits 4 min. Then 4 min. after the fast train leaves, the local train arrives & waits 3 min. If you arrive at the station at a random time during the rush period, find the probability that the fast train will be waiting and find the probability that no train will be there.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101416 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The fast train arrives every 15 minutes and waits 4 minutes.  That means that the fast train is there 4 out of every 15 minutes.  Pick a random minute out of any 15, and you have 4 possibilities out of 15 that the fast train will be there; probability <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F15 ALIGN=MIDDLE  ALT=\"4%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For the second part of the problem.  The fast train is at the station for a total of 4 minutes out of 15, and the local is there 3 minutes out of 15.  Since there is no overlap, the total time that any train is there is 7 minutes.  That means out of every 15 minutes, there are 8 minutes when there is no train there at all.  Hence, the probability of having to wait to get on a train is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F15 ALIGN=MIDDLE  ALT=\"8%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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