document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=953339>Question 953339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the events A and B:P(A) = 0.7,P(AUB)=0.9,P(A and B)=0.3 find P(-B and A) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582166 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(a and not b) is equal to .4.\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "p(a) = .7<BR>\n" );
document.write( "p(a or b) = .9<BR>\n" );
document.write( "p(a and b) = .3\r<BR>\n" );
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document.write( "the formula to use is:\r<BR>\n" );
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document.write( "p(a or b) = p(a) + p(b) - p(a and b)\r<BR>\n" );
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document.write( "replace p(a or b) with .9 and replace p(a) with .7 and replace p(a and b) with .3 and the formula becomes:\r<BR>\n" );
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document.write( ".9 = .7 + p(b) - .3\r<BR>\n" );
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document.write( "solve for p(b) to get p(b) = .5\r<BR>\n" );
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document.write( "since p(a) includes p(a and b), you have to remove p(a and b) to get p(a) only.\r<BR>\n" );
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document.write( "this results in p(a only) = .7 - .3 = .4\r<BR>\n" );
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document.write( "similarly, since p(b) includes p(a and b), you have to remove p(a and b) to get p(b) only.\r<BR>\n" );
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document.write( "this results in p(b only) = .5 - .3 = .2\r<BR>\n" );
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document.write( "your solution is that p(a and not b) is equal to p(a only) which is equal to .4\r<BR>\n" );
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document.write( "the following diagram show the relationship in pictures.\r<BR>\n" );
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document.write( "in this diagram, the set of c is defined as the set that contains all of the elements that are not in the set of a and also not in the set of b.\r<BR>\n" );
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document.write( "the probability of that occurring is defined as:\r<BR>\n" );
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document.write( "p(not(a or b)) = 1 - p(a or b) which becomes 1 - .9 which is equal to .1.\r<BR>\n" );
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document.write( "that's why the set of c has a probability of .1 associated with it.\r<BR>\n" );
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document.write( "from the diagram, you can see that the set of a intersects with the set of b and intersects with nothing else.\r<BR>\n" );
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document.write( "the set of (a and b) is defined as the intersection of the sets a and b.\r<BR>\n" );
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document.write( "those are the elements that are in set a and b at the same time.\r<BR>\n" );
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document.write( "take those away and you have the set of elements that are in set a and not in b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/030601.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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