document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151297>Question 1151297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A smartphone company found in a survey that 17% of people did not own a smartphone, 18% owned a smartphone only, 29% owned a smartphone and only a tablet, 21% owned a smartphone and only a computer, and 15% owned all three. If a person were selected at random, what is the probability that the person would own a smartphone only or a smartphone and computer only? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773026 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52780)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=773026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Honestly, I don't know and don't understand &nbsp;WHY &nbsp;the respectful tutor Jim chose this complicated way to solve the problem.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It can be solved in &nbsp;MUCH &nbsp;SIMPLER &nbsp;way, &nbsp;and I will show it to you now.\r<BR>\n" );
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document.write( "You have the universal set of all people surveyed.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Notice that &nbsp;17% + 18% + 29% + 21% + 15% = 100%, &nbsp;so these subsets cover the entire set.\r<BR>\n" );
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document.write( "Now, &nbsp;from the text, &nbsp;it should be clear to you that all listed categories of people are &nbsp;DISJOINT : <BR>\n" );
document.write( "the intersections between any two different categories are &nbsp;EMPTY.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is clear and obvious from the definitions of these categories in the post.\r<BR>\n" );
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document.write( "Now, &nbsp;the question is&nbsp;: &nbsp;&nbsp;what is the probability to randomly select from the union of the &nbsp;{18%} &nbsp;and &nbsp;{21%} &nbsp;subsets.\r<BR>\n" );
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document.write( "But of course, &nbsp;this probability is the sum  &nbsp;18% + 21% = 39%.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   <U>ANSWER</U>\r<BR>\n" );
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document.write( "It is a &nbsp;<U>DIRECT &nbsp;CONSEQUENCE</U> &nbsp;that the given categories \r<BR>\n" );
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document.write( "    a)  cover the entire universal set, &nbsp;&nbsp;&nbsp;&nbsp;and that\r\n" );
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document.write( "    b)  the categories are disjoint, i.e. have empty intersections.\r\n" );
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document.write( "It is fully consistent with the general formula of the Elementary probability theory\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;P(A U B) = P(A) + P(B) \r<BR>\n" );
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document.write( "for the disjoint events.\r<BR>\n" );
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document.write( "My solution is &nbsp;<U>completed</U> &nbsp;at this point.\r<BR>\n" );
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document.write( "A good style educational / (teaching) &nbsp;tradition assumes and requires that used teaching tools should not <BR>\n" );
document.write( "be more complicated than the problem itself.\r<BR>\n" );
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document.write( "Or, &nbsp;in other words, &nbsp;the solution should be &nbsp;AS &nbsp;SIMPLE &nbsp;AS &nbsp;POSSIBLE &nbsp;&nbsp;// &nbsp;&nbsp;still remaining to be correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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