document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75535>Question 75535</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0669417580/algebrahomeworkh>Precalculus with limits</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes, what is the probability that(a) exactly one is inserted and (b) at least one is inserted in the correct envelope </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54173 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=54173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes, what is the probability that(a) exactly one is inserted in the correct envelope:<BR>\n" );
document.write( "P(success)=1/4<BR>\n" );
document.write( "P(one correct of four)= 4C1 (1/4)^1(3/4)^3 = 4(27/256)=0.421875<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(b) at least one is inserted in the correct envelope<BR>\n" );
document.write( "P(at least one) = 1 - P(none correct)<BR>\n" );
document.write( "= 1 - 4C0(1/4)^0(3/4)^4 <BR>\n" );
document.write( "= 1 - 1*1*81/256 <BR>\n" );
document.write( "= 1 - 0.316<BR>\n" );
document.write( "= 0.6835<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );