document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530501>Question 530501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Out of 100 students, (49 girls, 51 boys) if three children are selected what is the probability that at least one is a girl?<BR>\n" );
document.write( "I am missing a key point to this equation because I keep getting 49/97 which I believe is wrong<BR>\n" );
document.write( "Thanks for any help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350103 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=350103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability of picking a girl on the first pick is:  49/100.<BR>\n" );
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document.write( "The probability of picking a girl on the second pick depends on whether a girl was picked first.<BR>\n" );
document.write( "If a girl was picked initially, then the probability of picking a girl on the second pick is :  48/99.<BR>\n" );
document.write( "If a boy was picked initially, then the probability of picking a girl on the second pick is:  49/99.<BR>\n" );
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document.write( "The probability of picking a girl first and second is: 49/100 * 48/99.<BR>\n" );
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document.write( "And so forth.<BR>\n" );
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document.write( "You need to determine the conditional probabilities to find the chance of picking at least 1 girl.<BR>\n" );
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document.write( "<th>1st Pick&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r\n" );
document.write( "<th>2nd Pick&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r\n" );
document.write( "<th>3rd Pick&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<th>Probability&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r\n" );
document.write( "<th>Description&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r\n" );
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document.write( "<td>P(girl)=49/100&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r\n" );
document.write( "<td>P(girl)=48/99&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r\n" );
document.write( "<td>P(girl)=47/98&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r\n" );
document.write( "<td>P=0.113939394\r\n" );
document.write( "<td>(A) 3 girls\r\n" );
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document.write( "<td>\"\r\n" );
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document.write( "<td>P(boy)=51/98\r\n" );
document.write( "<td>P=0.123636364\r\n" );
document.write( "<td>(B) 2 girls, 1 boy\r\n" );
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document.write( "<td>\"\r\n" );
document.write( "<td>P(boy)=51/99\r\n" );
document.write( "<td>P(girl)=48/98\r\n" );
document.write( "<td>P=0.123636364\r\n" );
document.write( "<td>(C) 2 girls, 1 boy\r\n" );
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document.write( "<td>\"\r\n" );
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document.write( "<td>P(boy)=50/98\r\n" );
document.write( "<td>P=0.128787879\r\n" );
document.write( "<td>(D) 1 girl, 2 boys\r\n" );
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document.write( "<td>P(boy)=51/100\r\n" );
document.write( "<td>P(girl)=49/99\r\n" );
document.write( "<td>P(girl)=48/98\r\n" );
document.write( "<td>P=0.123636364\r\n" );
document.write( "<td>(E) 2 girls, 1 boy\r\n" );
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document.write( "<td>\"\r\n" );
document.write( "<td>\"\r\n" );
document.write( "<td>P(boy)=50/98\r\n" );
document.write( "<td>P=0.128787879\r\n" );
document.write( "<td>(F) 1 girl, 2 boys</tr>\r\n" );
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document.write( "<td>\"\r\n" );
document.write( "<td>P(boy)=50/99\r\n" );
document.write( "<td>P(girl)=49/98\r\n" );
document.write( "<td>P=0.128787879\r\n" );
document.write( "<td>(G) 1 girl, 2 boys\r\n" );
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document.write( "<td>P(boy)=49/98\r\n" );
document.write( "<td>P=0.128787879\r\n" );
document.write( "<td>(H) 3 boys\r\n" );
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document.write( "The total probability = 1.00, as you can see.<BR>\n" );
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document.write( "P(at least 1 girl) = A+B+C+D+E+F+G = 0.871212121<BR>\n" );
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document.write( "<b>OR</b><BR>\n" );
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document.write( "You could see the problem in terms of the chance of picking 3 boys.  If you do <b>not</b> pick 3 boys, then you have to pick at least 1 girl.<BR>\n" );
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document.write( "P(picking 3 boys) = 51/100 * 50/99 * 49/98 = 0.128787879<BR>\n" );
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document.write( "P(picking at least 1 girl) = 1.0 - 0.128787879 = 0.871212121<BR>\n" );
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document.write( "Same answer. Two ways to get there.<BR>\n" );
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document.write( "Done.<BR>\n" );
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