document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203559>Question 1203559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P(A) = P(B) = 1/3 and P(A n B) 1/10, Find the following:<BR>\n" );
document.write( "A) P(B')<BR>\n" );
document.write( "B) P(A u B')<BR>\n" );
document.write( "C) P(B n A')<BR>\n" );
document.write( "D) P(A' u B') </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839216 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=839216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Problem 1\r<BR>\n" );
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document.write( "Use the complement law of probability<BR>\n" );
document.write( "P(B') = 1 - P(B)<BR>\n" );
document.write( "P(B') = 1 - (1/3)<BR>\n" );
document.write( "P(B') = <font color=red size=4>2/3</font>\r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "Law of total probability<BR>\n" );
document.write( "P(A) = P(A n B) + P(A n B')<BR>\n" );
document.write( "rearrange it to<BR>\n" );
document.write( "P(A n B') = P(A) - P(A n B)<BR>\n" );
document.write( "Check out this question for more info<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1203558.html\">https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1203558.html</a><BR>\n" );
document.write( "refer to problem 1 of that link\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "P(A u B') = P(A) + P(B') - P(A n B') ...... inclusion-exclusion principle<BR>\n" );
document.write( "P(A u B') = P(A) + P(B') - [P(A) - P(A n B)] ...... use rule mentioned above<BR>\n" );
document.write( "P(A u B') = P(A) + P(B') - P(A) + P(A n B)<BR>\n" );
document.write( "P(A u B') = P(B') + P(A n B)<BR>\n" );
document.write( "P(A u B') = (2/3) + (1/10)<BR>\n" );
document.write( "P(A u B') = (20/30) + (3/30)<BR>\n" );
document.write( "P(A u B') = (20+3)/30<BR>\n" );
document.write( "P(A u B') = <font color=red size=4>23/30</font>\r<BR>\n" );
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document.write( "Problem 3\r<BR>\n" );
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document.write( "Use a similar trick I did in the previous problem to determine that<BR>\n" );
document.write( "P(B n A') = P(B) - P(B n A)<BR>\n" );
document.write( "which is the same as<BR>\n" );
document.write( "P(B n A') = P(B) - P(A n B)\r<BR>\n" );
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document.write( "Furthermore<BR>\n" );
document.write( "P(B n A') = P(B) - P(A n B)<BR>\n" );
document.write( "P(B n A') = (1/3) - (1/10)<BR>\n" );
document.write( "P(B n A') = (10/30) - (3/30)<BR>\n" );
document.write( "P(B n A') = (10-3)/30<BR>\n" );
document.write( "P(B n A') = <font color=red size=4>7/30</font>\r<BR>\n" );
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document.write( "Problem 4\r<BR>\n" );
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document.write( "P(A' u B') = P( (A n B)' )  ... De Morgans Law<BR>\n" );
document.write( "P(A' u B') = 1 - P(A n B) ... complement law<BR>\n" );
document.write( "P(A' u B') = 1 - (1/10)<BR>\n" );
document.write( "P(A' u B') = (10/10) - (1/10)<BR>\n" );
document.write( "P(A' u B') = (10-1)/10<BR>\n" );
document.write( "P(A' u B') = <font color=red size=4>9/10</font><BR>\n" );
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