document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983386>Question 983386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag has 7 balls: a green, black, blue, brown, pink, red, and orange one. If 6 balls are removed from the bag at random, what is the probability that a blue ball has been removed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604166 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=604166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say we had 6 slots A through F\r<BR>\n" );
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document.write( "7 choices for slot A<BR>\n" );
document.write( "6 choices for slot B<BR>\n" );
document.write( "5 choices for slot C<BR>\n" );
document.write( "4 choices for slot D<BR>\n" );
document.write( "3 choices for slot E<BR>\n" );
document.write( "2 choices for slot F\r<BR>\n" );
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document.write( "7*6*5*4*3*2 = 5040\r<BR>\n" );
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document.write( "If order mattered, then there would be 5040 ways to pick the six balls. However, order doesn't matter so we divide by 6! = 720 to get 5040/720 = 7\r<BR>\n" );
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document.write( "There are 7 ways to pick the six balls (out of a pool of 7), where again, order doesn't matter.\r<BR>\n" );
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document.write( "If we reserve a slot, say slot A, for a blue ball, then there are 5 slots left and 6 items to fill those slots.\r<BR>\n" );
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document.write( "Using the same idea above, we can take a shortcut using the <a  rel=nofollow HREF=\"http://www.mathwords.com/c/combination_formula.htm\">combination formula</a> to say 6 C 5 = 6\r<BR>\n" );
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document.write( "There are 6 ways to pick a set of balls where one is definitely blue. \r<BR>\n" );
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document.write( "This is out of 7 ways total to pick the balls (we don't care if we get blue or not here)\r<BR>\n" );
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document.write( "That's why the answer is 6/7\r<BR>\n" );
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document.write( "Alternative Method:\r<BR>\n" );
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document.write( "Think of it in a reverse way. Think of it as \"what is the probability of blue NOT being chosen?\". In other words, \"what is the probability of blue being left in the bag?\"\r<BR>\n" );
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document.write( "Well that's simply 1/7. There is a 1 in 7 chance of picking blue, so there is a 1/7 chance that blue remains in the bag.\r<BR>\n" );
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document.write( "That means there is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2F7+=+6%2F7 ALIGN=MIDDLE  ALT=\"1-1%2F7+=+6%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > chance that blue is not in the bag. \r<BR>\n" );
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document.write( "Either way, the final answer is 6/7 </SPAN>\n" );
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