document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119555>Question 1119555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the following information below to answer the next two questions.<BR>\n" );
document.write( "In a particular town, 30% of all adults have brown hair.  \r<BR>\n" );
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document.write( "18. If three adults are randomly and independently selected for a survey, calculate the probability that all three have brown hair.<BR>\n" );
document.write( "(a) 0.300<BR>\n" );
document.write( "(b) 0.027<BR>\n" );
document.write( "(c) 0.090  <BR>\n" );
document.write( "(d) 0.900 \r<BR>\n" );
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document.write( "19. If two adults are randomly and independently selected for a survey, calculate the probability that at least one has brown hair.<BR>\n" );
document.write( "(a) 0.49<BR>\n" );
document.write( "(b) 0.51<BR>\n" );
document.write( "(c) 0.70<BR>\n" );
document.write( "(d) 0.39<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 #735178 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=735178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this looks like a binomial distribution type of problem.\r<BR>\n" );
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document.write( "p = .3 equals probability that a person has brown hair.<BR>\n" );
document.write( "q = 1 - p = .7 equsls probability that a person doesn't have brown hair.\r<BR>\n" );
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document.write( "the formula is p(x) = c(n,x) * p^2 * q^(n-x)\r<BR>\n" );
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document.write( "in the first problem, n = 3 and you are looking for the probability that all 3 have brown hair.\r<BR>\n" );
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document.write( "formula becomes p(3) = .3^3 * .7^0 * c(3,3).\r<BR>\n" );
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document.write( "this is equal to .027 * 1 * 1 = .027\r<BR>\n" );
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document.write( "that would be selection b.\r<BR>\n" );
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document.write( "in the second problem, n = 2 and you are looking for the probability that at least 1 has brown hair.\r<BR>\n" );
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document.write( "that would be equal to 1 minus the probability that all 2 do not have brown hair.\r<BR>\n" );
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document.write( "formula becomes p(0) = .3^0 * .7^2 * c(2,0).\r<BR>\n" );
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document.write( "this is equal to 1 * .49* 1 = .49\r<BR>\n" );
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document.write( "that's the probability that none have brown hair.\r<BR>\n" );
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document.write( "the probability that at least 1 has brown hair would be 1 minus .49 = .51\r<BR>\n" );
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document.write( "that would be selection b.\r<BR>\n" );
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document.write( "the complete probabilities should always add up to 1.\r<BR>\n" );
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document.write( "those complete probabilities are shown in the following excel printout.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/070905.jpg\" alt=\"$$$\" ><BR>\n" );
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