document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=403748>Question 403748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alice and Bob work on a math problem independently. The probability that Alice solves the<BR>\n" );
document.write( "problem is 0.8 and the probability that Bob solves it is 0.6.<BR>\n" );
document.write( "(a) What is the probability that both solve the problem?<BR>\n" );
document.write( "(b) What is the probability that neither solves it?<BR>\n" );
document.write( "(c) What is the probability that exactly one of them solves it?<BR>\n" );
document.write( "(d) Given that exactly one of them solves the problem, what is the probability that it is<BR>\n" );
document.write( "Bob?\r<BR>\n" );
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document.write( "A string of Christmas lights has 20 bulbs and if any bulb fails then the whole string goes out.<BR>\n" );
document.write( "Suppose that each bulb has a 5% chance of failure during the Christmas holidays and that<BR>\n" );
document.write( "the 20 bulbs are independent of each other.<BR>\n" );
document.write( "What is the probability that the string of lights will go out during the holidays? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285465 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=285465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alice and Bob work on a math problem independently. The probability that Alice solves the problem is 0.8 and the probability that Bob solves it is 0.6.<BR>\n" );
document.write( "(a) What is the probability that both solve the problem?:0.6*0.8<BR>\n" );
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document.write( "(b) What is the probability that neither solves it?:0.4*0.2<BR>\n" );
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document.write( "(c) What is the probability that exactly one of them solves it?<BR>\n" );
document.write( "Ans: 1 - [0.48+0.08] = 0.44 <BR>\n" );
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document.write( "(d) Given that exactly one of them solves the problem, what is the probability that it is Bob?<BR>\n" );
document.write( "Ans: P(Bob|one solves) = P(Bob AND one solves)/P(one solves) <BR>\n" );
document.write( "= (0.6*0.2)/0.44 = 0.27<BR>\n" );
document.write( "----------------------------------- <BR>\n" );
document.write( "A string of Christmas lights has 20 bulbs and if any bulb fails then the whole string goes out.<BR>\n" );
document.write( "Suppose that each bulb has a 5% chance of failure during the Christmas holidays and that the 20 bulbs are independent of each other.<BR>\n" );
document.write( "What is the probability that the string of lights will go out during the holidays?<BR>\n" );
document.write( "P(failure) = 0.05<BR>\n" );
document.write( "P(not fail) = 0.95<BR>\n" );
document.write( "Ans: P(string out) = 1 - P(none fail) = 1-0.95^20 = 0.6415<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============ </SPAN>\n" );
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