document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204405>Question 1204405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey of 500 people was conducted to determine how many people own a pet, and how many people own a car. The results showed that 300 people own a pet, 150 people own a car, and 100 people own both a pet and a car. What is the probability that a randomly selected person owns a pet or a car?<BR>\n" );
document.write( "P(A or B) = P(A) + P(B) - P(A and B) where P(A) is the probability of owning a pet, P(B) is the probability of owning a car, and P(A and B) is the probability of owning both a pet and a car.  Is the answer .70 or .72?\r<BR>\n" );
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document.write( "300/500 + 150/500 - 100/500 = 350/500 = 7/10 = .70\r<BR>\n" );
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document.write( "300/500 = .60 ; 150/500 = .30 ; (1  -  (.60 + .30) = .10 own both a pet a and car\r<BR>\n" );
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document.write( ".60 + .30  -  (.60 * .30) <BR>\n" );
document.write( "0.90  -  0.18 = 0.72<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840626 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "A = set of people who own a pet (some also own a car)<BR>\n" );
document.write( "B = set of people who own a car (some also own a pet)\r<BR>\n" );
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document.write( "n(A) = number of people in set A<BR>\n" );
document.write( "n(A) = 300<BR>\n" );
document.write( "n(B) = 150<BR>\n" );
document.write( "n(A and B) = 100\r<BR>\n" );
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document.write( "Use the inclusion-exclusion principle:<BR>\n" );
document.write( "n(A or B) = n(A) + n(B) - n(A and B)<BR>\n" );
document.write( "n(A or B) = 300 + 150 - 100<BR>\n" );
document.write( "n(A or B) = 350<BR>\n" );
document.write( "We subtract off 100 because those people were counted twice when computing the n(A)+n(B) portion. The 100 goes in the overlapped portion of the Venn Diagram.\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "P(A or B) = n(A or B)/n(Total)<BR>\n" );
document.write( "P(A or B) = 350/500<BR>\n" );
document.write( "P(A or B) = <font color=red>0.7</font>\r<BR>\n" );
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document.write( "A slightly different approach\r<BR>\n" );
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document.write( "n(A) = 300<BR>\n" );
document.write( "n(A and B) = 100<BR>\n" );
document.write( "n(A only) = n(A) - n(A and B) = 300-100 = 200<BR>\n" );
document.write( "There are 200 people who own a pet, but do not own a car.<BR>\n" );
document.write( "This value 200 goes in circle A but outside circle B of the Venn Diagram.\r<BR>\n" );
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document.write( "n(B) = 150<BR>\n" );
document.write( "n(A and B) = 100<BR>\n" );
document.write( "n(B only) = n(B) - n(A and B) = 150-100 = 50<BR>\n" );
document.write( "There are 50 people who own a car, but do not own a pet.<BR>\n" );
document.write( "This value 50 goes in circle B but outside circle A of the Venn Diagram.\r<BR>\n" );
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document.write( "n(A or B) = n(A only) + n(B only) + n(A and B)<BR>\n" );
document.write( "n(A or B) = 200 + 50 + 100<BR>\n" );
document.write( "n(A or B) = 350<BR>\n" );
document.write( "There are 350 people who own a pet, have a car, or both.\r<BR>\n" );
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document.write( "The steps from this point onward will be the same as the previous section above.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>0.7</font><BR>\n" );
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