document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758179>Question 758179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A really bad carton of 18 eggs contains 7 spoiled eggs. An unsuspecting chef picks 4 eggs at random<BR>\n" );
document.write( "for his “Mega-Omelet Surprise.” Find the probability that the number of unspoiled eggs among the<BR>\n" );
document.write( "4 selected is<BR>\n" );
document.write( "a. exactly 4 b. 2 or fewer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461398 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=461398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n = 18<BR>\n" );
document.write( "7 are spoiled<BR>\n" );
document.write( "chef picks 4 out of the 18.<BR>\n" );
document.write( "possible combinations are 18C4 = 3060\r<BR>\n" );
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document.write( "probability that he will get 4 spoiled eggs is equal to 7C4 / 18C4 which is equal to 35 / 3060.\r<BR>\n" );
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document.write( "probabiltiy that he can get 0 spoiled eggs is equal to 11C4 / 3060 which is equal to 330 / 3060.\r<BR>\n" );
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document.write( "probabiltiy that he can get 1 spoiled egg is equal to (7C1 * 11C3) / 18C4 which is equal to (7 * 165) / 3060 which is equal to 1155 / 3060.\r<BR>\n" );
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document.write( "probabiltiy that he can get 2 spoiled eggs is equal to (7C2 * (11C2) / 18C4 which is equal to (21 * 55) / 3060 which is equal to 1155 / 3060.\r<BR>\n" );
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document.write( "probabiltiy that he can get 0 or 1 or 2 spoiled eggs is equal to (330 + 1155 + 1155) / 3060 which is equal to 2640 / 3060.\r<BR>\n" );
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document.write( "this is impossible to visualize with so many eggs.<BR>\n" );
document.write( "reduce the problem and we may be able to visualize how the solution is obtained.<BR>\n" );
document.write( "suppose 5 eggs of which 3 are spoiled.\r<BR>\n" );
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document.write( "chef draws 2 eggs.<BR>\n" );
document.write( "what is the probability that both are bad?<BR>\n" );
document.write( "what is the probability that 0 or 1 are bad?\r<BR>\n" );
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document.write( "probability of both eggs being spoiled would be equal to:\r<BR>\n" );
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document.write( "3C2 / 5C2 which is equal to 3 / 10\r<BR>\n" );
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document.write( "label the eggs:\r<BR>\n" );
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document.write( "s1<BR>\n" );
document.write( "s2<BR>\n" );
document.write( "s3<BR>\n" );
document.write( "g1<BR>\n" );
document.write( "g2\r<BR>\n" );
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document.write( "possible combinations of 2 eggs out of 5 is shown below:\r<BR>\n" );
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document.write( "s1, s2   ***** 2 eggs spoiled<BR>\n" );
document.write( "s1, s3   ***** 2 eggs spoiled<BR>\n" );
document.write( "s1, g1 <BR>\n" );
document.write( "s1, g2<BR>\n" );
document.write( "s2, s3   ***** 2 eggs spoiled<BR>\n" );
document.write( "s2, g1<BR>\n" );
document.write( "s2, g2<BR>\n" );
document.write( "s3, g1<BR>\n" );
document.write( "s3, g2<BR>\n" );
document.write( "g1, g2\r<BR>\n" );
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document.write( "the formula works for 2 spoiled eggs.\r<BR>\n" );
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document.write( "probability of getting 0 spoiled eggs is equal to 2C2 / 5C2 which is equal to 1 / 10.\r<BR>\n" );
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document.write( "the total possible combinations are, once again:\r<BR>\n" );
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document.write( "s1, s2   <BR>\n" );
document.write( "s1, s3   <BR>\n" );
document.write( "s1, g1 <BR>\n" );
document.write( "s1, g2<BR>\n" );
document.write( "s2, s3   <BR>\n" );
document.write( "s2, g1<BR>\n" );
document.write( "s2, g2<BR>\n" );
document.write( "s3, g1<BR>\n" );
document.write( "s3, g2<BR>\n" );
document.write( "g1, g2   ***** 0 eggs spoiled\r<BR>\n" );
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document.write( "probability of getting 0 spoiled eggs is 1 out of 10.\r<BR>\n" );
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document.write( "probability of getting 1 spoiled egg is equal to (3C1 * 2C1) / 5C2 which is equal to (3 * 2) / 10 which is equal to 6 / 10\r<BR>\n" );
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document.write( "the total possible combinations are, once again:\r<BR>\n" );
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document.write( "s1, s2   <BR>\n" );
document.write( "s1, s3   <BR>\n" );
document.write( "s1, g1   ***** 1 egg spoiled <BR>\n" );
document.write( "s1, g2   ***** 1 egg spoiled<BR>\n" );
document.write( "s2, s3<BR>\n" );
document.write( "s2, g1   ***** 1 egg spoiled<BR>\n" );
document.write( "s2, g2   ***** 1 egg spoiled<BR>\n" );
document.write( "s3, g1   ***** 1 egg spoiled<BR>\n" );
document.write( "s3, g2   ***** 1 egg spoiled<BR>\n" );
document.write( "g1, g2\r<BR>\n" );
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document.write( "the formulas can be demonstrated to work with small numbers.<BR>\n" );
document.write( "this isn't possible with big numbers.<BR>\n" );
document.write( "some logic needs to be applied to convince yourself that the same formulas will work with bigger number.<BR>\n" );
document.write( "the rest is on faith that your logic is good.\r<BR>\n" );
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document.write( "probability of getting 0 or 1 spoiled egg out of 5 is equal to 1/10 + 6/10 which is equal to 7/10 as shown below:\r<BR>\n" );
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document.write( "s1, s2   <BR>\n" );
document.write( "s1, s3   <BR>\n" );
document.write( "s1, g1   ***** 1 egg spoiled <BR>\n" );
document.write( "s1, g2   ***** 1 egg spoiled<BR>\n" );
document.write( "s2, s3<BR>\n" );
document.write( "s2, g1   ***** 1 egg spoiled<BR>\n" );
document.write( "s2, g2   ***** 1 egg spoiled<BR>\n" );
document.write( "s3, g1   ***** 1 egg spoiled<BR>\n" );
document.write( "s3, g2   ***** 1 egg spoiled<BR>\n" );
document.write( "g1, g2   ***** 0 eggs spoiled\r<BR>\n" );
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document.write( " </SPAN>\n" );
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