document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=566685>Question 566685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From experience, Teton Tire knows the probability is .95 that a particular XB-70 tire will last 60,000 miles before it becomes bald or fails. An adjustment is made on any tire that does not last 60,000 miles. You purchase 4 XB-70’s.<BR>\n" );
document.write( "a.	(10 pts) What is the probability that all 4 tires will last at least 60,000 miles?  \r<BR>\n" );
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document.write( "b.	(10 pts) What is the probability that none of the tires will last at least 60,000 miles? \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 #366312 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=366312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> probability that all 4 tires will last at least 60,000 miles is .95^4 = .81450625<BR>\n" );
document.write( "probability that all 4 tires will not last at least 60,000 miles is 1 - .81450625 = .18549375<BR>\n" );
document.write( "probability that none of the tires will last at least 60,000 miles is .05^4 = 6.25 * 10^-6<BR>\n" );
document.write( "the total probabilities are shown below:<BR>\n" );
document.write( "p(4 last 60,000) = 4C0 * .95^4 * .05^0 = 1 * .95^4 * .05^0 = .81450625<BR>\n" );
document.write( "p(3 last 60,000) = 4C1 * .95^3 * .05^1 = 4 * .95^3 * .05^1 = .l71475<BR>\n" );
document.write( "p(2 last 60,000) = 4C2 * .95^2 * .05^2 = 6 * .95^2 * .05^2 = .0135375<BR>\n" );
document.write( "P(1 last 60,000) = 4C3 * .95^1 * .05^3 = 4 * .95^1 * .05^3 = 4.75 * 10^-4<BR>\n" );
document.write( "p(0 last 60,000) - 4C4 * .95^0 * .05^4 = 1 * .95^0 * .05^4 = 6.25 * 10^-6<BR>\n" );
document.write( "add all these probabilities together and you get a total probability of 1.<BR>\n" );
document.write( "the probability that 4 last 60,000 is.81450625.<BR>\n" );
document.write( "the probability that 0 last 60,000 is 6.25 * 10^-6.<BR>\n" );
document.write( "the probability that 4 do not last 60,000 is equal to 1 - .81450625 = .18549375.<BR>\n" );
document.write( "this is the probability that 0 and 1 and 2 and 3 last 60,000 which is the total probability minus the probability that 4 last 60,000 miles.<BR>\n" );
document.write( "you were asked:<BR>\n" );
document.write( "a.	(10 pts) What is the probability that all 4 tires will last at least 60,000 miles?<BR>\n" );
document.write( "answer is.81450625<BR>\n" );
document.write( "b.	(10 pts) What is the probability that none of the tires will last at least 60,000 miles?<BR>\n" );
document.write( "answer is 6.25 * 10^-6 which is equivalent to .00000625\r<BR>\n" );
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