document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084512>Question 1084512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are ten cards labelled 1 to 10. Jacky takes out two cards without replacing them. Find the probability that both show even numbers.\r<BR>\n" );
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document.write( "Thanks! Much appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698604 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=698604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\">For problems like these, I find it helps to make a table like this one (shown below):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/Dqps1t3.png\"><BR>\n" );
document.write( "Table generated with Excel. Free alternative programs (such as OpenOffice) can do the same thing.\r<BR>\n" );
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document.write( "The top row represents the possible choices for the first draw. <BR>\n" );
document.write( "The left border of values represent the choices for the second draw. <BR>\n" );
document.write( "Any ordered pair of the form (x,y) represents a possible outcome for both cards. <BR>\n" );
document.write( "For instance, in cell D9 we have the ordered pair (x,y) = (2,7) meaning that x = 2 is the first value drawn and y = 7 is the next value. <BR>\n" );
document.write( "The other ordered pairs in the table are to be read in this similar way.\r<BR>\n" );
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document.write( "Note: Something like (x,y) = (2,2) is NOT possible because once we pick x = 2, we don't replace it. <BR>\n" );
document.write( "It would be impossible to draw '2' again so the choices for y would go from {1,2,3,4,5,6,7,8,9,10} to {1,3,4,5,6,7,8,9,10}. <BR>\n" );
document.write( "Whenever this sort of event happens, I will mark it as NA (as seen in the table above)\r<BR>\n" );
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document.write( "Now go through the table and record all of the instances where BOTH x and y are even numbers\r<BR>\n" );
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document.write( "Here is that list of outcomes highlighted with double asterisks on each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/0ZYh14d.png\"><BR>\n" );
document.write( "That highlighted list of ordered pairs is\r<BR>\n" );
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document.write( "(4,2)<BR>\n" );
document.write( "(6,2)<BR>\n" );
document.write( "(8,2)<BR>\n" );
document.write( "(10,2)<BR>\n" );
document.write( "(2,4)<BR>\n" );
document.write( "(6,4)<BR>\n" );
document.write( "(8,4)<BR>\n" );
document.write( "(10,4)<BR>\n" );
document.write( "(2,6)<BR>\n" );
document.write( "(4,6)<BR>\n" );
document.write( "(8,6)<BR>\n" );
document.write( "(10,6)<BR>\n" );
document.write( "(2,8)<BR>\n" );
document.write( "(4,8)<BR>\n" );
document.write( "(6,8)<BR>\n" );
document.write( "(10,8)<BR>\n" );
document.write( "(2,10)<BR>\n" );
document.write( "(4,10)<BR>\n" );
document.write( "(6,10)<BR>\n" );
document.write( "(8,10)\r<BR>\n" );
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document.write( "There are <font color=blue>20</font> values in the list above. \r<BR>\n" );
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document.write( "There would be 10*10 = 100 outcomes if replacements were made, but no replacements are made meaning we have 10 copies of \"NA\" to subtract out. So we have 100-10 = <font color=green>90</font> outcomes total.\r<BR>\n" );
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document.write( "Dividing the values (<font color=blue>20</font> and <font color=green>90</font>) we get: <font color=blue>20</font>/<font color=green>90</font> = 2/9 = 0.222222 = 22.2222%\r<BR>\n" );
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document.write( "Final Answer as a fraction: <font color=red>2/9</font> (this is exact)<BR>\n" );
document.write( "Final Answer as a decimal value: <font color=red>0.222222</font> (this is approximate)<BR>\n" );
document.write( "Final Answer as a percentage: <font color=red>22.2222%</font> (this is approximate)\r<BR>\n" );
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document.write( "Notes: <BR>\n" );
document.write( "* Use a calculator, or long division, to go from the fraction 2/9 to the decimal 0.222222<BR>\n" );
document.write( "* To go from the decimal value to the percentage, move the decimal point 2 spots to the right.<BR>\n" );
document.write( "* The three answer formats all represent the same idea just expressed different ways. <BR>\n" );
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