document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135273>Question 135273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a<BR>\n" );
document.write( "fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of<BR>\n" );
document.write( "a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent<BR>\n" );
document.write( "events. Why might the assumption of independence be violated? (b) Why might a driver be<BR>\n" );
document.write( "tempted not to use a seat belt “just on this trip”? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99087 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=99087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. <BR>\n" );
document.write( "(a) What is the probability of a fatal accident over a lifetime? <BR>\n" );
document.write( "P = np = 1/4000000 * 50000 = 0.0125<BR>\n" );
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document.write( "Explain your reasoning carefully. Hint: Assume independent<BR>\n" );
document.write( "events.<BR>\n" );
document.write( "Each trip is a binomial experiment; you either have an accident or you don't.<BR>\n" );
document.write( "The expected value = np = # of trials * probability of \"success\" on each trial.<BR>\n" );
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document.write( "Why might the assumption of independence be violated? <BR>\n" );
document.write( "Hopefully a person becomes a more careful driver as he gains more experience.<BR>\n" );
document.write( "so the probability of having an accicentchanges with experience.<BR>\n" );
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document.write( "(b) Why might a driver be tempted not to use a seat belt “just on this trip”?<BR>\n" );
document.write( "He might look at the enormously small probability of an accident on this trip<BR>\n" );
document.write( "and conclude the low probability somehow protects him.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );