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 #772995 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=772995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Problem<BR>\n" );
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document.write( "A smartphone company found in a survey that <BR>\n" );
document.write( "17% of people did not own a smartphone<BR>\n" );
document.write( "18% owned a smartphone only<BR>\n" );
document.write( "29% owned a smartphone and only a tablet<BR>\n" );
document.write( "21% owned a smartphone and only a computer<BR>\n" );
document.write( "15% owned all three. <BR>\n" );
document.write( "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?<BR>\n" );
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document.write( "Draw out a Venn Diagram which consists of a rectangle and inside the rectangle will go 3 overlapping circles as shown below<BR>\n" );
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document.write( "S = set of people who own smartphones<BR>\n" );
document.write( "T = set of people who own tablets<BR>\n" );
document.write( "C = set of people who own computers<BR>\n" );
document.write( "U = universal set = set of all people surveyed\r<BR>\n" );
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document.write( "There are 8 distinct regions of this Venn Diagram. The regions are (a) through (h) and are defined as such:<BR>\n" );
document.write( "<ul><li>Region (a) = People who own smartphones only</li><li>Region (b) = People who own smartphones and tablets only (no computers)</li><li>Region (c) = People who own tablets only</li><li>Region (d) = People who own smartphones and computers only (no tablets)</li><li>Region (e) = People who own all three devices: smartphone, tablet, computer</li><li>Region (f) = People who own tablets and computers only (no smartphone)</li><li>Region (g) = People who own computers only</li><li>Region (h) = People who do not own a smartphone, do not own a tablet, do not own a computer.</li></ul>\r<BR>\n" );
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document.write( "Let's list out the facts that we are given<BR>\n" );
document.write( "<ul><li>Fact 1: 17% of people did not own a smartphone</li><li>Fact 2: 18% owned a smartphone only</li><li>Fact 3: 29% owned a smartphone and only a tablet</li><li>Fact 4: 21% owned a smartphone and only a computer</li><li>Fact 5: 15% owned all three.</li></ul><BR>\n" );
document.write( "We won't be using fact 1 to solve this current problem. If you're curious about it, then this represents the sum of regions (h), (g), (f), and (c) added up. In other words, it is the total sum of people outside of circle S.\r<BR>\n" );
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document.write( "From fact 2, we can fill in region (a) with 18%<BR>\n" );
document.write( "From fact 3, we can fill in region (b) with 29%<BR>\n" );
document.write( "From fact 4, we can fill in region (d) with 21%<BR>\n" );
document.write( "From fact 5, we can fill in region (e) with 15%\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/6X2pckX.png\">\r<BR>\n" );
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document.write( "We're being asked \"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?\". \r<BR>\n" );
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document.write( "This is a two part question<BR>\n" );
document.write( "Part A: what is the probability that the person would own a smartphone only<BR>\n" );
document.write( "Part B: what is the probability that the person would own a smartphone and computer only?\r<BR>\n" );
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document.write( "The answer to part A is 18% as this is region (a) found earlier. The answer to part B is 21% which is the value in region (d). <BR>\n" );
document.write( "Adding these percentages up gets us 18+21 = 39%. We can add the percentages like this because the regions (a) through (h) are mutually exclusive regions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/3NcQEkK.png\"> \r<BR>\n" );
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document.write( "So 39% of the people surveyed either own a smartphone only, or they own a smartphone and a computer only.\r<BR>\n" );
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document.write( "The probability of randomly selecting a person that either owns a smartphone only, or they own a smartphone and a computer only is <font color=red size=4>39%</font>. In decimal form that would convert to 0.39, and as a fraction it would be 39/100. These all represent the same answer, just written in a different form. \r<BR>\n" );
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