document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185781>Question 1185781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5.2.10<BR>\n" );
document.write( "The proportion of brown M&M’s in a milk chocolate packet is approximately 14% (Madison, 2013).  Suppose a package of M&M’s typically contains 52 M&M’s.<BR>\n" );
document.write( "a.) State the random variable.<BR>\n" );
document.write( "b.)	Argue that this is a binomial experiment<BR>\n" );
document.write( "Find the probability that <BR>\n" );
document.write( "c.)	Six M&M’s are brown.<BR>\n" );
document.write( "d.)	Twenty-five M&M’s are brown.<BR>\n" );
document.write( "e.)	All of the M&M’s are brown.<BR>\n" );
document.write( "f.)	Would it be unusual for a package to have only brown M&M’s?  If this were to happen, what would you think is the reason?\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 #816616 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=816616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n = 52<BR>\n" );
document.write( "p = .14<BR>\n" );
document.write( "q = 1 minus p = .86<BR>\n" );
document.write( "p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "p(6) = .14^6 * .86^46 * c(52,6) = 0.148745273\r<BR>\n" );
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document.write( "p(25) = .14^25 * .86^27 * c(52,25) = 3.66167 * 10^-9\r<BR>\n" );
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document.write( "p(52) = .14^52 * .86^0 * c(52,52) = 3.96879E * 10^-45\r<BR>\n" );
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document.write( "if you round your answers to 8 decimal places, those higher numbers become effectively 0.\r<BR>\n" );
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document.write( "i used excel to show all the probabilities.<BR>\n" );
document.write( "the sum of those probabilities is equal to 1, as it should be.<BR>\n" );
document.write( "note that the higher probbilitie are effectively equal to 0 when the results are rounded to 8 decimal digits.\r<BR>\n" );
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document.write( "here's the excel printout.\r<BR>\n" );
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document.write( "it would be unusual for a packet to have all brown m&m's.<BR>\n" );
document.write( "the most likely cause would be that the other colors ran out and so there were only brown colors left.<BR>\n" );
document.write( "this could be the result of machine failure or human failure.<BR>\n" );
document.write( "maybe somebody forgot to load the other colors?\r<BR>\n" );
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