document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468803>Question 468803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 1: In a large population, 63 % 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?\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 #321642 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The situation where at least one out of 4 are vaccinated includes all but one possibility, that which none of the 4 are vaccinated.<BR>\n" );
document.write( "The sum of all probabilities must equal 1.<BR>\n" );
document.write( "Let Q be probability none of the 4 are vaccinated.<BR>\n" );
document.write( "Let P be probability that at least 1 is vaccinated.<BR>\n" );
document.write( "P = 1 - Q<BR>\n" );
document.write( "Now if 63% are vaccinated, then 37% are not vaccinated.<BR>\n" );
document.write( "Thus any given person has a probability of 0.37 of not being vaccinated.<BR>\n" );
document.write( "Q = (0.37)^4 = 0.0187<BR>\n" );
document.write( "P = 1 - 0.0187 = 0.981 </SPAN>\n" );
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