document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=663913>Question 663913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You pick 5 apples from a grocery store owned by the professor. The probability of a randomly chosen apple being rotten is 0.518. Let X represent the number of apples that are NOT rotten. Find the probability of X=k in the table below.\r<BR>\n" );
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document.write( "k 	P(X = k)<BR>\n" );
document.write( "0 	<BR>\n" );
document.write( "1 	<BR>\n" );
document.write( "2 	<BR>\n" );
document.write( "3 	<BR>\n" );
document.write( "4 	<BR>\n" );
document.write( "5 \r<BR>\n" );
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document.write( "I tried multiplying .482*0 then .482*1 all the way down the table.	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413040 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=413040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability of a randomly chosen apple being rotten is 0.518\r<BR>\n" );
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document.write( "So the probability of a randomly chosen apple NOT being rotten is 1 - 0.518 = 0.482\r<BR>\n" );
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document.write( "So p = 0.482\r<BR>\n" );
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document.write( "There are 5 apples picked, so n = 5.\r<BR>\n" );
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document.write( "This is a binomial distribution problem, so use the formula P(X = k) = (n C x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "For k = 0\r<BR>\n" );
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document.write( "P(X = k) = (n C x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 0) = (5 C 0)*(0.482)^(0)*(1-0.482)^(5-0)\r<BR>\n" );
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document.write( "P(X = 0) = (5 C 0)*(0.482)^(0)*(0.518)^(5-0)\r<BR>\n" );
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document.write( "P(X = 0) = (1)*(0.482)^(0)*(0.518)^5\r<BR>\n" );
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document.write( "P(X = 0) = (1)*(1)*(0.037294844329568)\r<BR>\n" );
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document.write( "P(X = 0) = 0.037294844329568\r<BR>\n" );
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document.write( "P(X = 0) = 0.03729\r<BR>\n" );
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document.write( "For k = 1\r<BR>\n" );
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document.write( "P(X = k) = (n C x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 1) = (5 C 1)*(0.482)^(1)*(1-0.482)^(5-1)\r<BR>\n" );
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document.write( "P(X = 1) = (5 C 1)*(0.482)^(1)*(0.518)^(5-1)\r<BR>\n" );
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document.write( "P(X = 1) = (5)*(0.482)^(1)*(0.518)^4\r<BR>\n" );
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document.write( "P(X = 1) = (5)*(0.482)*(0.071997768976)\r<BR>\n" );
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document.write( "P(X = 1) = 0.17351462323216\r<BR>\n" );
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document.write( "P(X = 1) = 0.17351\r<BR>\n" );
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document.write( "For k = 2\r<BR>\n" );
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document.write( "P(X = k) = (n C x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 2) = (5 C 2)*(0.482)^(2)*(1-0.482)^(5-2)\r<BR>\n" );
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document.write( "P(X = 2) = (5 C 2)*(0.482)^(2)*(0.518)^(5-2)\r<BR>\n" );
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document.write( "P(X = 2) = (10)*(0.482)^(2)*(0.518)^3\r<BR>\n" );
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document.write( "P(X = 2) = (10)*(0.232324)*(0.138991832)\r<BR>\n" );
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document.write( "P(X = 2) = 0.32291138377568\r<BR>\n" );
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document.write( "P(X = 2) = 0.32291\r<BR>\n" );
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document.write( "For k = 3\r<BR>\n" );
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document.write( "P(X = k) = (n C x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 3) = (5 C 3)*(0.482)^(3)*(1-0.482)^(5-3)\r<BR>\n" );
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document.write( "P(X = 3) = (5 C 3)*(0.482)^(3)*(0.518)^(5-3)\r<BR>\n" );
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document.write( "P(X = 3) = (10)*(0.482)^(3)*(0.518)^2\r<BR>\n" );
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document.write( "P(X = 3) = (10)*(0.111980168)*(0.268324)\r<BR>\n" );
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document.write( "P(X = 3) = 0.30046966598432\r<BR>\n" );
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document.write( "P(X = 3) = 0.30047\r<BR>\n" );
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document.write( "For k = 4\r<BR>\n" );
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document.write( "P(X = k) = (n C x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 4) = (5 C 4)*(0.482)^(4)*(1-0.482)^(5-4)\r<BR>\n" );
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document.write( "P(X = 4) = (5 C 4)*(0.482)^(4)*(0.518)^(5-4)\r<BR>\n" );
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document.write( "P(X = 4) = (5)*(0.482)^(4)*(0.518)^1\r<BR>\n" );
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document.write( "P(X = 4) = (5)*(0.053974440976)*(0.518)\r<BR>\n" );
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document.write( "P(X = 4) = 0.13979380212784\r<BR>\n" );
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document.write( "P(X = 4) = 0.13979\r<BR>\n" );
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document.write( "and finally, for k = 5\r<BR>\n" );
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document.write( "P(X = k) = (n C x)*(p)^(x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "P(X = 5) = (5 C 5)*(0.482)^(5)*(1-0.482)^(5-5)\r<BR>\n" );
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document.write( "P(X = 5) = (5 C 5)*(0.482)^(5)*(0.518)^(5-5)\r<BR>\n" );
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document.write( "P(X = 5) = (1)*(0.482)^(5)*(0.518)^0\r<BR>\n" );
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document.write( "P(X = 5) = (1)*(0.026015680550432)*(1)\r<BR>\n" );
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document.write( "P(X = 5) = 0.026015680550432\r<BR>\n" );
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document.write( "P(X = 5) = 0.02602\r<BR>\n" );
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document.write( "The updated table is then\r<BR>\n" );
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document.write( "<TABLE  BORDER=1 CELLPADDING=10>\n" );
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document.write( "<TR>\r\n" );
document.write( "  <TH>k</TH>\r\n" );
document.write( "  <TH>P(X = k)</TH>\r\n" );
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document.write( "  <TD >0</TD>\r\n" );
document.write( "  <TD >0.03729</TD>\r\n" );
document.write( "</TR>\r\n" );
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document.write( "  <TD >1</TD>\r\n" );
document.write( "  <TD >0.17351</TD>\r\n" );
document.write( "</TR>\r\n" );
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document.write( "  <TD >2</TD>\r\n" );
document.write( "  <TD >0.32291</TD>\r\n" );
document.write( "</TR>\r\n" );
document.write( "<TR>\r\n" );
document.write( "  <TD >3</TD>\r\n" );
document.write( "  <TD >0.30047</TD>\r\n" );
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document.write( "  <TD >4</TD>\r\n" );
document.write( "  <TD >0.13979</TD>\r\n" );
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document.write( "  <TD >5</TD>\r\n" );
document.write( "  <TD >0.02602</TD>\r\n" );
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document.write( "</TABLE>\r<BR>\n" );
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document.write( "How to read the table above. Let's say you look at the third row. In this row is <font color=\"red\">2</font> and <font color=\"green\">0.32291</font>, which says \"the probability of picking exactly <font color=\"red\">2</font> rotten apples (out of 5 total) is roughly <font color=\"green\">0.32291</font> or 32.291% </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );