document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125217>Question 1125217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains three 20-dollar bills, three 10-dollar bills, and three 5-dollar bills. Three bills are selected from the bag at random. Let the random variable X represent the total dollar value of the selected bills. \r<BR>\n" );
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document.write( "What is the least possible value of X? <BR>\n" );
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document.write( "What is the greatest possible value of X? <BR>\n" );
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document.write( "What is Pr(X=30)? <BR>\n" );
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document.write( "Enter your answers as whole numbers or fractions in lowest terms. Your answers should all be numeric -- do not use dollar signs in your answers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741614 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bag contains three 20-dollar bills, three 10-dollar bills, and three 5-dollar bills. Three bills are selected from the bag at random. Let the random variable X represent the total dollar value of the selected bills. \r<BR>\n" );
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document.write( "What is the least possible value of X?<br> <BR>\n" );
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document.write( "This happens when all three selections are each $5 bills, 3x5 = 15:<BR>\n" );
document.write( "Ans:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+15+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+15+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  dollars<br>\r<BR>\n" );
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document.write( "What is the greatest possible value of X? <BR>\n" );
document.write( "This happens when all three selections are $20 bills:  3x20 = 60:<BR>\n" );
document.write( "Ans:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+60+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+60+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  dollars<br> \r<BR>\n" );
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document.write( "What is Pr(X=30)? <BR>\n" );
document.write( "Let F=five, T=ten, W=twenty selected  \r<BR>\n" );
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document.write( "Lets list the probabilities where a ten is selected first, then any of {F,T,W} for the remaining two:<BR>\n" );
document.write( "Pr(TTT) = (3/9)(2/8)(1/7) = 6/504  <BR>\n" );
document.write( "Pr(TTF) = (3/9)(2/8)(3/7) = 18/504 <BR>\n" );
document.write( "Pr(TTW) = (3/9)(2/8)(3/7) = 18/504 <BR>\n" );
document.write( "Pr(TWW) = 18/504<BR>\n" );
document.write( "Pr(TFF) = 18/504<BR>\n" );
document.write( "Pr(TWF) = 27/504<BR>\n" );
document.write( "Pr(TFW) = 27/504<BR>\n" );
document.write( "Pr(TFT) =  18/504<BR>\n" );
document.write( "Pr(TWT) = 18/504<br>\r<BR>\n" );
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document.write( "Similarly for Pr(F,*,*) and Pr(W,*,*)      (not shown, but they follow the same pattern, for instance if you want Pr(F,W,F) just look above for Pr(T,W,T), mentally substituting \"F\" for \"T\" and you can see it is  18/504) <br>\r<BR>\n" );
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document.write( "Pr(X=30) = Pr(three tens)  +  Pr(two fives and one twenty)<BR>\n" );
document.write( "Pr(X=30) = Pr(T,T,T) + Pr(F,F,W) + Pr(F,W,F) + Pr(W,F,F)<BR>\n" );
document.write( "                =   6/504 +   18/504 + 18/504 + 18/504<BR>\n" );
document.write( "                =  60/504<BR>\n" );
document.write( "                =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+5%2F42+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+5%2F42+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (about 0.1190 or 11.9%)\r<BR>\n" );
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