document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218189>Question 218189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five balls are numbered with the integers 1 through 5 and placed in a jar. Three are drawn without replacement. What is the probability that the sum of the three integers on the balls is odd? Express your answer as a common fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164338 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=164338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> integers 1 through 5<BR>\n" );
document.write( "sum of 3 numbers is odd if:<BR>\n" );
document.write( "2 are even and 1 is odd<BR>\n" );
document.write( "3 are odd<BR>\n" );
document.write( "no other combination will work.<BR>\n" );
document.write( "3 even gives even <BR>\n" );
document.write( "2 odd and 1 even gives even<BR>\n" );
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document.write( "there are 3 odds in there (1,3,5)<BR>\n" );
document.write( "there are 2 evens in there (2,4)<BR>\n" );
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document.write( "PROBABILITY OF GETTING 2 EVENS AND 1 ODD<BR>\n" );
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document.write( "probability of getting 2 evens and 1 odd are:<BR>\n" );
document.write( "2/5 * 1/4 * 3/3<BR>\n" );
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document.write( "you can get this in 3 ways.<BR>\n" );
document.write( "they would be:<BR>\n" );
document.write( "first draw is odd, second draw is odd, third draw is even.<BR>\n" );
document.write( "first draw is odd, second draw is even, third draw is odd.<BR>\n" );
document.write( "first draw is even, second draw is odd, third draw is odd.<BR>\n" );
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document.write( "the probability of each one of these occurrences is the same.<BR>\n" );
document.write( "it is 2/5 * 1/4 * 3/3 = .1<BR>\n" );
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document.write( "the total probability for getting 2 even and 1 odd is 3 * .1 = .3<BR>\n" );
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document.write( "PROBABILITY OF GETTING 3 ODDS<BR>\n" );
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document.write( "The probability for getting 3 odds are:<BR>\n" );
document.write( "3/5 * 2/4 * 1/3<BR>\n" );
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document.write( "you can get this in 1 way.<BR>\n" );
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document.write( "the total probability for getting 3 odds = .1<BR>\n" );
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document.write( "PROBABILITY OF GETTING 3 ODDS OR 2 EVENS AND 1 ODD<BR>\n" );
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document.write( "This equals .3 + .1 = .4<BR>\n" );
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document.write( "You have a 40% probability of getting an odd number sum for 3 numbers drawn out of the numbers 1,2,3,4,5<BR>\n" );
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