document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=666108>Question 666108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a large population, 59 % of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #414265 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=414265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We never like \"at least one\" in probability theory. Always be thinking complement with it. Because the complement of at least one is NONE. \r<BR>\n" );
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document.write( "Using our binomial theorem, we want to choose 0 out of the 4. \r<BR>\n" );
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document.write( "(4 choose 0) * (.59)^0  * (1-.59)^4 = .0283\r<BR>\n" );
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document.write( "Now remember, this is the probability for none, so we need to take turn the complement back into our original.\r<BR>\n" );
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document.write( "So the P[at least one] = 1-P[none] = 1 - .0283 = .9717\r<BR>\n" );
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document.write( "Hope this helps! </SPAN>\n" );
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