document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185647>Question 1185647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fruit grower claims that 2/3 of his mango crop has been contaminated by a fruit fly infestation. Find the probability that of the next four mangoes inspected by this grower, 1 to 3 m  inclusive of mangoes are contaminated </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816487 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=816487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = 2/3 = probability any mango picked at random is contaminated.<BR>\n" );
document.write( "q = 1 - 2/3 = 1/3 = probability any mango picked at random is not contaminated.\r<BR>\n" );
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document.write( "binomial probability states that:\r<BR>\n" );
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document.write( "p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "if n = 4, then the total probabilities will be:\r<BR>\n" );
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document.write( "p(0) + p(1) + p(2) + p(3) + p(4).\r<BR>\n" );
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document.write( "p(1) = (2/3)^1 * (1/3)^(4-1 = 3) * c(4,1) = .098765432<BR>\n" );
document.write( "p(2) = (2/3)^2 * (1/3)^(4-2 = 2) * c(4,2) = .296296296<BR>\n" );
document.write( "p(3) = (2/3)^3 * (1/3)^(4-3 = 1) * c(4,3) = .395061728\r<BR>\n" );
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document.write( "add them up and the probability of 1 to 3 rotten fruits out of 4 = .790123457.\r<BR>\n" );
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document.write( "the total probabilities are equal to 1 as shown below.\r<BR>\n" );
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document.write( "p(0) =	0.012345679\r\n" );
document.write( "p(1) =	0.098765432\r\n" );
document.write( "p(2) =	0.296296296\r\n" );
document.write( "p(3) =	0.395061728\r\n" );
document.write( "p(4) =	0.197530864\r\n" );
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document.write( "p(total) = 	1\r\n" );
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document.write( "p(1,2,3) =	0.790123457\r\n" );
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document.write( "c(n,x) is the number of ways you can get x elements out of a set of n.\r<BR>\n" );
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document.write( "the formula is c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "c(4,3) is equal to 4! / (3! * 1!) = (4 * 3!) / (3! * 1!) = 4 / 1 = 4.\r<BR>\n" );
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document.write( "1! is always equal to 1<BR>\n" );
document.write( "0! is always equal to 1 as well.\r<BR>\n" );
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document.write( "as an example, p(0) = (2/3)^0 * (1/3)^4 * c(4,0) = 1 * .012345679 * 1 = .012345679.\r<BR>\n" );
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document.write( "your solution is that the probability of getting 1 to 3 contaminated mangoes is equal to .790123457.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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