document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171689>Question 1171689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If P(A)=0.5, P(B)=0.5 and P(A \textrm{ and } B)= 0.05, find the following probabilities:<BR>\n" );
document.write( "a)   P(A \textrm{ or } B) = \r<BR>\n" );
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document.write( "b)   P( \textrm{not }A )  = \r<BR>\n" );
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document.write( "c)   P( \textrm{not }B ) = \r<BR>\n" );
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document.write( "d)   P( A \textrm{ and } (\textrm{not }B) )  = \r<BR>\n" );
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document.write( "e)   P( \textrm{not }(A \textrm{ and } B)) = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796616 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=796616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Draw out a Venn diagram with circles A and B overlapping. Both of these circles are inside a rectangle representing the universal set (U).\r<BR>\n" );
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document.write( "Let's say there are 100 people. Place 50 of them in circle A and 50 in circle B. This produces P(A) = 50/100 = 0.5 and P(B) = 0.5 for the same reasons.\r<BR>\n" );
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document.write( "Place 5 in the overlapping region to indicate P(A and B) = 5/100 = 0.05\r<BR>\n" );
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document.write( "Note how 50-5 = 45 people are in circle A, but outside circle B. A similar situation happens with B as well.\r<BR>\n" );
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document.write( "There are 45+5+45 = 95 people in either circle, or both. This leaves 100-95 = 5 outside both circles, but inside the universal set.\r<BR>\n" );
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document.write( "We have this Venn diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/WGsuK3x.png\">\r<BR>\n" );
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document.write( "Use that diagram to answer the questions below\r<BR>\n" );
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document.write( "P(A or B) = (45+5+45)/100 = 95/100 = 0.95<BR>\n" );
document.write( "We add up all the values in the circles, then divide by 100\r<BR>\n" );
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document.write( "P(not A) = (45+5)/100 = 50/100 = 0.50<BR>\n" );
document.write( "We're adding everything that isn't in circle A\r<BR>\n" );
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document.write( "P(not B) = (45+5)/100 = 50/100 = 0.50<BR>\n" );
document.write( "Same idea as P(not A), but now add up everything that isn't in circle B.\r<BR>\n" );
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document.write( "P(A and not B) = 45/100 = 0.45<BR>\n" );
document.write( "Only the value 45 is in circle A but outside circle B\r<BR>\n" );
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document.write( "P(not(A and B)) = (45+45+5)/100 = 95/100 = 0.95<BR>\n" );
document.write( "We add up the 45's outside the shared overlapped region, plus that 5 outside both circles.<BR>\n" );
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