document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126252>Question 1126252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"If something can go wrong, it will go wrong.\" This funny saying is called Murphy's law. Let's interpret this to mean \"If something can go wrong, there is a very high probability that it will eventually go wrong.\" \r<BR>\n" );
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document.write( "Suppose we look at the event of having an automobile accident at some time during a day's commute. Let's assume that the probability of having an accident on a given day is 1 in a thousand or 0.001. That is, in your town, one of every thousand cars on a given day is involved in an accident (including little fender-benders). We also assume that having (or not having) an accident on a given day is independent of having (or not having) an accident on any other given day. Suppose you commute 46 weeks per year, 5 days a week, for a total of 230 days each year. In the following parts, write each probability in decimal form rounded to three places. <BR>\n" );
document.write( "(a) What is the probability that you have no accident over a year's time? <BR>\n" );
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document.write( "(b) What is the probability that you have at least one accident over a one-year period? <BR>\n" );
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document.write( "(c) Repeat part (a) for a 10-year period and for a 30-year period. <BR>\n" );
document.write( "10-year period     <BR>\n" );
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document.write( "30-year period     <BR>\n" );
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document.write( "Repeat part (b) for a 10-year period and for a 30-year period. <BR>\n" );
document.write( "10-year period     <BR>\n" );
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document.write( "30-year period     <BR>\n" );
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document.write( "(d) Does your work support the idea that there is a mathematical basis for Murphy's law as we interpreted it? <BR>\n" );
document.write( "Yes, even though the possibility of a crash is slim, the probability of an event over a long period of time is large. <BR>\n" );
document.write( "Yes, the possibility of a crash is large and the probability of an event over a long period of time is large.     <BR>\n" );
document.write( "No, even though the possibility of a crash is large, the probability of an event over a long period of time is slim. <BR>\n" );
document.write( "No, the possibility of a crash is slim and the probability of an event over a long period of time is sli </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742593 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=742593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> probability of no accident on a given day is 0.999<BR>\n" );
document.write( "For a year of 230 days, that probability of no accident is 0.999^230=0.7944\r<BR>\n" );
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document.write( "For 10 years, it would be 0.1001<BR>\n" );
document.write( "For 30 years, it would be 0.0010\r<BR>\n" );
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document.write( "At least one accident has a probability of 1-prob(no accident) or 0.2056 year1\r<BR>\n" );
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document.write( "For 10 years,it would be 0.8999<BR>\n" );
document.write( "For 30 years, it would be 0.9990\r<BR>\n" );
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document.write( "The first part is closest--low probability events that over a long period of time have an expected value > 0 will eventually happen.  Expected value here is probability * time </SPAN>\n" );
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