document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083927>Question 1083927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a box containing 25 item 5 of which are defective, 4 are chosern at random ,let X be the number of defective items found.Obtain the probability distribution of X if <BR>\n" );
document.write( "I. the items are chosen with replacement.<BR>\n" );
document.write( "II. the items are chosen with out replacement.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698015 by </B><A HREF=/tutors/aboutme.mpl?userid=natolino_2017><B>natolino_2017(77)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=natolino_2017><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=698015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I) with replacement\r<BR>\n" );
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document.write( "x: number of defective in 4 picking.\r<BR>\n" );
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document.write( "Range of x ={0,1,2,3,4}\r<BR>\n" );
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document.write( "Every picking is independent from the rest.\r<BR>\n" );
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document.write( "p= P(pick one defective) = number of defective/total items = 5/25 =1/5.\r<BR>\n" );
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document.write( "x is binomial (n= 4, p=1/5).\r<BR>\n" );
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document.write( "P(x=0) = 4C0(p^0)(1-p)^(4-0) = 256/625.<BR>\n" );
document.write( "P(x=1) = 4C1(p^1)(1-p)^(4-1) = 256/625.<BR>\n" );
document.write( "P(x=2) = 4C2(p^2)(1-p)^(4-2) = 96/625.<BR>\n" );
document.write( "P(x=3) = 4C3(p^3)(1-p)^(4-3) = 16/625.<BR>\n" );
document.write( "P(x=4) = 4C4(p^4)(1-p)^(4-4) = 1/625.\r<BR>\n" );
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document.write( "II) without replacement\r<BR>\n" );
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document.write( "y: number of defective in 4 picking.\r<BR>\n" );
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document.write( "Range of y ={0,1,2,3,4}\r<BR>\n" );
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document.write( "y is hyper-geometric with N=25, n=4, d=5.\r<BR>\n" );
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document.write( "P(y=0) = (5C0)((25-5)C(4-0))/(25C4) = 969/2530.<BR>\n" );
document.write( "P(y=1) = (5C1)((25-5)C(4-1))/(25C4) = 114/253<BR>\n" );
document.write( "P(y=2) = (5C2)((25-5)C(4-2))/(25C4) = 38/253<BR>\n" );
document.write( "P(y=3) = (5C3)((25-5)C(4-3))/(25C4) = 4/253<BR>\n" );
document.write( "P(y=4) = (5C4)((25-5)C(4-4))/(25C4) = 1/2530\r<BR>\n" );
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document.write( "check for yourself that, in both results, the sum of every probabilities is equal to one.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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