document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085166>Question 1085166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A lecturer wants to select two students at random from a class of 7 males and 3 females. What is the probability the two students chosen are female?\r<BR>\n" );
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document.write( "Select one:<BR>\n" );
document.write( "A. 0.09<BR>\n" );
document.write( "B. 0.22<BR>\n" );
document.write( "C. 0.3<BR>\n" );
document.write( "D. 0.67 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699206 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=699206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\"><BR>\n" );
document.write( "Let<BR>\n" );
document.write( "A = number of ways to choose 2 females<BR>\n" );
document.write( "B = number of ways to choose 2 people (any gender)\r<BR>\n" );
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document.write( "Order will not matter. \r<BR>\n" );
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document.write( "There are 3 ways to pick 2 females. Let's consider the group of females {X,Y,Z} where the letters are codenames for their actual names<BR>\n" );
document.write( "The three groups we can form are: {X,Y}, {Y,Z}, {X,Z}<BR>\n" );
document.write( "Each group in a set of curly braces<BR>\n" );
document.write( "Note how order does not matter. Something like {X,Y} is the same as {Y,X}\r<BR>\n" );
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document.write( "An alternative viewpoint is to consider that there are 3 ways to not pick a female. The three cases would be {X}, {Y}, and {Z}\r<BR>\n" );
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document.write( "If you wish to use a formula, then you can use the nCr combination formula to get<BR>\n" );
document.write( "n C r = (n!)/(r!*(n-r)!)<BR>\n" );
document.write( "3 C 2 = (3!)/(2!*(3-2)!)<BR>\n" );
document.write( "3 C 2 = (3!)/(2!*1!)<BR>\n" );
document.write( "3 C 2 = (3*2!)/(2!*1!)<BR>\n" );
document.write( "3 C 2 = (3)/(1!)<BR>\n" );
document.write( "3 C 2 = (3)/(1)<BR>\n" );
document.write( "3 C 2 = 3/1<BR>\n" );
document.write( "3 C 2 = 3<BR>\n" );
document.write( "So that confirms the previous results<BR>\n" );
document.write( "In this case, n = 3 because there are three applicants to choose from and r = 2 because that's the number of selections made\r<BR>\n" );
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document.write( "So far, we know that A = 3 because there are three ways to pick two women (from a pool of 3).\r<BR>\n" );
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document.write( "Using the same formula, but now with n = 10 (there are 10 people total), we get<BR>\n" );
document.write( "n C r = (n!)/(r!*(n-r)!)<BR>\n" );
document.write( "10 C 2 = (10!)/(2!*(10-2)!)<BR>\n" );
document.write( "10 C 2 = (10!)/(2!*8!)<BR>\n" );
document.write( "10 C 2 = (10*9*8!)/(2!*8!)<BR>\n" );
document.write( "10 C 2 = (10*9)/(2!)<BR>\n" );
document.write( "10 C 2 = (10*9)/(2*1)<BR>\n" );
document.write( "10 C 2 = 90/2<BR>\n" );
document.write( "10 C 2 = 45\r<BR>\n" );
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document.write( "Indicating that there are 45 different unique groups we can form if we do not worry about the gender of who is selected.\r<BR>\n" );
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document.write( "This means that B = 45\r<BR>\n" );
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document.write( "Now divide the values A and B to get A/B = 3/45 = 1/15\r<BR>\n" );
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document.write( "The probability as a fraction is 1/15. Don't forget to fully reduce. This value is exact.\r<BR>\n" );
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document.write( "Because your teacher wants the answer in decimal form, you would use a calculator or long division to get 1/15 = 0.06666666666667 which is approximate. That value rounds to 0.067\r<BR>\n" );
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document.write( "Because this answer isn't listed, I'm assuming there's a typo somewhere. A guess I have is that choice D should be 0.067 instead of 0.67\r<BR>\n" );
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document.write( "Or perhaps choice D should be 0.07 instead of 0.67\r<BR>\n" );
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document.write( "In any event, I'm thinking your teacher meant to have the answer be choice D. I would check with the teacher though.\r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">choice D) 0.67</font><BR>\n" );
document.write( "Note: Look at the section above for an explanation\r<BR>\n" );
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document.write( "Edit: MathLover1's solution makes sense on the surface, but looking at it closer there's a flaw in the logic. The answer (3/10)*(3/10) = 9/100 = 0.09 would only apply if the first applicant chosen is put back into the pool. It doesn't make sense to select the same applicant twice.<BR>\n" );
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