document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200399>Question 1200399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Each child born to a particular set of parents has a probability of 0.25 of having <BR>\n" );
document.write( "blood type O. If these parents have 5 children. What is the probability that?<BR>\n" );
document.write( "a. Exactly three of them have blood type O.<BR>\n" );
document.write( "b. At most 2 have blood type O<BR>\n" );
document.write( "c. At least 4 have no blood type O<BR>\n" );
document.write( "d. The fifth child have blood type O<BR>\n" );
document.write( "e. Compute the mean and variance of this probability distribution<BR>\n" );
document.write( "f. Draw the probability distribution table<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 #834525 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The probability of exactly <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> independent trials with a uniform probability of success on any given trial of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(n,k,p)\ =\ {{n}\choose{k}}\,(p)^k(1\,-\,p)^{n-k}\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large {{n}\choose{k}}\"> is the number of combinations of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things taken <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> at a time.\r<BR>\n" );
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document.write( "The probability of at least <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> independent trials with a uniform probability of success on any given trial of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is given by the sum:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(n,\geq\,k,p)\ =\ \sum_{r=k}^n\,{{n}\choose{r}}\,(p)^r(1\,-\,p)^{n-r}\">\r<BR>\n" );
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document.write( "Which is the probability of exactly <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes plus the probability of exactly <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\,+\,1\"> and so on up to the probability of exactly n successes.\r<BR>\n" );
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document.write( "Just plug in your numbers, remembering to express the probability as a decimal, and do the indicated arithmetic.\r<BR>\n" );
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document.write( "It may save you some arithmetic if you recognize that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(n,\geq\,k,p)\ =\ 1\ -\ P(n,\leq\,k-1,p)\ =\ 1\ -\ \sum_{r=0}^{k-1}\,{{n}\choose{r}}\,(p)^r(1\,-\,p)^{n-r}\">\r<BR>\n" );
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document.write( "The mean of the binomial distribution is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large np\">, and the variance of the binomial distribution is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large np(1\,-\,p)\">\r<BR>\n" );
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document.write( "The distribution table would be the the list of results for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 5\"> for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\ =\"> zero through five.\r<BR>\n" );
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document.write( "													John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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