document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175613>Question 1175613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you are to pick a number from the box with numbers 1-30, what is the probability that you will pick a number that is odd or is divisible by 5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801250 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=801250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 15 odd numbers: 1,3,5,...,29<BR>\n" );
document.write( "there are 6 numbers divisible by 5:  5,10,15,20,25,30<BR>\n" );
document.write( "there are 3 numbers that are both:   5,15,25<br>\r<BR>\n" );
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document.write( "P(odd or number divisible by 5) = 15/30 + 6/30 - 3/30 = 18/30 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28+3%2F5+%29+ ALIGN=MIDDLE  ALT=\"highlight%28+3%2F5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "If you are wondering why the subtraction, the intersection needs to be subtracted once because it is included in each of the other two probabilities (i.e. it is counted twice).<BR>\n" );
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document.write( "A second way to look at it is to find independent sets, then there is no intersection and we can just add things.  We have the 15 odd numbers { 1,3,5,...,29 }  + even numbers divisible by 5: { 10,20,30 }  which makes 18 total results of interest: 18/30 = 3/5, as above.  <br>\r<BR>\n" );
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document.write( "The first method is more general (inclusion-exclusion principle) and is far more powerful when there are many overlapping sets.\r<BR>\n" );
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