document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113823>Question 1113823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sam is fond of taking long-distance trips. During each trip his car has a tire failure in each 100-mile stretch with a probability of 0.05. He recently embarked on an 800-mile trip and took two spare tires with him on the trip.<BR>\n" );
document.write( "a. What is the probability that the first change of tire occurred 300 miles from his starting point?<BR>\n" );
document.write( "b. What is the probability that his second change of tire occurred 500 miles from his starting point?<BR>\n" );
document.write( "c. What is the probability that he completed the trip without having to change tires? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728899 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Sam is fond of taking long-distance trips. During each trip his car has a tire failure in each 100-mile stretch with a probability of 0.05. He recently embarked on an 800-mile trip and took two spare tires with him on the trip.<BR>\n" );
document.write( "a. What is the probability that the first change of tire occurred 300 miles from his starting point?<BR>\n" );
document.write( "Event description:: (no)(no)(yes) = 0.95^2*0.05 = 0.0451<BR>\n" );
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document.write( "b. What is the probability that his second change of tire occurred 500 miles from his starting point?<BR>\n" );
document.write( "Event description: (one in the 1st 400 miles)*(0.05)<BR>\n" );
document.write( "= 4C1*0.05*0.95^4 * 0.05<BR>\n" );
document.write( "= 4*0.05*0.8145*0.05<BR>\n" );
document.write( "= 0.008145<BR>\n" );
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document.write( "c. What is the probability that he completed the trip without having to change tires?<BR>\n" );
document.write( "0.95^8 = 0.6634<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );