document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=874099>Question 874099</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher of a specific species of birds knows from experience that  70% of such birds find	hidden sources of food immediately after being released.  If the researcher releases 15 such birds,  calculate the probability that exactly 5 of them find hidden sources of food.						 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527301 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=527301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> probability of success = .7 = p<BR>\n" );
document.write( "probability of failure = 1 - .7 = .3 = q<BR>\n" );
document.write( "n = 15<BR>\n" );
document.write( "x = number of successes.\r<BR>\n" );
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document.write( "p(x) = nCx * p^x * q^(n-x)\r<BR>\n" );
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document.write( "replace values for variables in this formula to get:\r<BR>\n" );
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document.write( "p(5) = 15C5 * .7^5 * .3^10\r<BR>\n" );
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document.write( "15C5 = 3003\r<BR>\n" );
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document.write( "p(5) = 3003 * .16807 * .0000059049\r<BR>\n" );
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document.write( "p(5) = .002980287\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "the probabilities for 1,2,3,4,5,6,..... are in the attached table.\r<BR>\n" );
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document.write( "the sum of the probabilities should be equal to 1 or something went wrong.\r<BR>\n" );
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document.write( "this table is good since the probabilities do sum up to be equal to 1.\r<BR>\n" );
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document.write( "n	x	p	q	p^x	q^(n-x)	        nCx	p(x)\r\n" );
document.write( "15	0	0.7	0.3	1.00	0.000000014349	1	0.000000014349\r\n" );
document.write( "15	1	0.7	0.3	0.70	0.000000047830	15	0.000000502212\r\n" );
document.write( "15	2	0.7	0.3	0.49	0.000000159432	105	0.000008202792\r\n" );
document.write( "15	3	0.7	0.3	0.34	0.000000531441	455	0.000082939340\r\n" );
document.write( "15	4	0.7	0.3	0.24	0.000001771470	1365	0.000580575378\r\n" );
document.write( "15	5	0.7	0.3	0.17	0.000005904900	3003	0.002980286939\r\n" );
document.write( "15	6	0.7	0.3	0.12	0.000019683000	5005	0.011590004761\r\n" );
document.write( "15	7	0.7	0.3	0.08	0.000065610000	6435	0.034770014284\r\n" );
document.write( "15	8	0.7	0.3	0.06	0.000218700000	6435	0.081130033329\r\n" );
document.write( "15	9	0.7	0.3	0.04	0.000729000000	5005	0.147235986413\r\n" );
document.write( "15	10	0.7	0.3	0.03	0.002430000000	3003	0.206130380978\r\n" );
document.write( "15	11	0.7	0.3	0.02	0.008100000000	1365	0.218623131340\r\n" );
document.write( "15	12	0.7	0.3	0.01	0.027000000000	455	0.170040213264\r\n" );
document.write( "15	13	0.7	0.3	0.01	0.090000000000	105	0.091560114835\r\n" );
document.write( "15	14	0.7	0.3	0.01	0.300000000000	15	0.030520038278\r\n" );
document.write( "15	15	0.7	0.3	0.00	1.000000000000	1	0.004747561510\r\n" );
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document.write( "					total probability >>>	1.000000000000\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "15C5 comes from the combination formula of nCx = n! / (x! * (n-1)!)\r<BR>\n" );
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document.write( "n! is equal to 15!\r<BR>\n" );
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document.write( "x! is equal to 5!\r<BR>\n" );
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document.write( "(n-x)! is equal to (15 - 5)! = 10!\r<BR>\n" );
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document.write( "nCx formula becomes 15! / (5! * 10!) = 3003\r<BR>\n" );
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document.write( " </SPAN>\n" );
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