document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=601511>Question 601511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you throw a pair of dice eight times, what is the probability that you will get \"doubles\" more then once? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379820 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=379820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability of getting doubles is p = 6/36 = 1/6 = 0.1667\r<BR>\n" );
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document.write( "Let's compute the probability of getting doubles x = 0 and x = 1 time. To find this, you would use the binomial probability distribution formula.\r<BR>\n" );
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document.write( "P(X = x) = (n ncr x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 0) = (8 ncr 0)*(0.1667)^(0)*(1-0.1667)^(8-0)\r<BR>\n" );
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document.write( "P(X = 0) = (8 ncr 0)*(0.1667)^(0)*(0.8333)^(8-0)\r<BR>\n" );
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document.write( "P(X = 0) = (1)*(0.1667)^(0)*(0.8333)^8\r<BR>\n" );
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document.write( "P(X = 0) = (1)*(1)*(0.232494)\r<BR>\n" );
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document.write( "P(X = 0) = 0.232494\r<BR>\n" );
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document.write( "P(X = x) = (n ncr x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 1) = (8 ncr 1)*(0.1667)^(1)*(1-0.1667)^(8-1)\r<BR>\n" );
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document.write( "P(X = 1) = (8 ncr 1)*(0.1667)^(1)*(0.8333)^(8-1)\r<BR>\n" );
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document.write( "P(X = 1) = (8)*(0.1667)^(1)*(0.8333)^7\r<BR>\n" );
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document.write( "P(X = 1) = (8)*(0.1667)*(0.2790035137489)\r<BR>\n" );
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document.write( "P(X = 1) = 0.372079\r<BR>\n" );
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document.write( "Now add these final results:\r<BR>\n" );
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document.write( "0.232494 + 0.372079\r<BR>\n" );
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document.write( "0.604573\r<BR>\n" );
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document.write( "So P(X <= 1)  =   0.604573\r<BR>\n" );
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document.write( "Now subtract this from 1 to find P(X > 1)\r<BR>\n" );
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document.write( "P(X > 1) =  1 - P(X <= 1)\r<BR>\n" );
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document.write( "P(X > 1) =  1 - 0.604573\r<BR>\n" );
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document.write( "P(X > 1) =  0.395427\r<BR>\n" );
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document.write( "So the probability that you will get \"doubles\" more than once is roughly 0.395427 </SPAN>\n" );
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