document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126741>Question 126741</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 fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt “just on this trip”?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92853 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we say that the probability of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+fatal ALIGN=MIDDLE  ALT=\"+fatal\"   DISABLED_style= \"max-width:90%; height:auto;\" > accidents in a lifetime is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the probability of having one (or more) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=fatal ALIGN=MIDDLE  ALT=\"fatal\"   DISABLED_style= \"max-width:90%; height:auto;\" > accidents in a lifetime is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we have:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1-P=1-%283999999%2F4000000%29%5E50000+=0.0124 ALIGN=MIDDLE  ALT=\"p=1-P=1-%283999999%2F4000000%29%5E50000+=0.0124\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2 ALIGN=MIDDLE  ALT=\"1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >%)\r<BR>\n" );
document.write( "\n" );
document.write( "-or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+p+=P ALIGN=MIDDLE  ALT=\"1+-+p+=P\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is the probability that you survive each and every journey\r<BR>\n" );
document.write( "\n" );
document.write( "a)\r<BR>\n" );
document.write( "\n" );
document.write( "Why the independence assumption might be violated?\r<BR>\n" );
document.write( "\n" );
document.write( "hmmm, that is more question of “psychology” then statistics\r<BR>\n" );
document.write( "\n" );
document.write( "-overconfidence, less care when driving, doing other things in same time, and \r<BR>\n" );
document.write( "\n" );
document.write( "so on, could cause <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "(b) Why might a driver be tempted not to use a seat belt “just on this trip”?\r<BR>\n" );
document.write( "\n" );
document.write( "it might be he/she was thinking about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<BR>\n" );
document.write( "(:-))))\r<BR>\n" );
document.write( "\n" );
document.write( "many drivers think \"it didn't happened to me never before, so it shouldn't happen now too\"<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );