document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=570955>Question 570955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose A and b are events such that P(A)=1/3, P(B)= 1/3, and P(Aor B)=1/2. complete parts (a) and (b) below.<BR>\n" );
document.write( "a. are events A and B mutually exclusive ? explain your answer.<BR>\n" );
document.write( "b. determine P(A &B).<BR>\n" );
document.write( "P(A& B) = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367869 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=367869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "Two events A and B are mutually exclusive when P(A or B) = P(A) + P(B). \r<BR>\n" );
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document.write( "So let's plug in the given values to see if that's indeed true.\r<BR>\n" );
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document.write( "P(A or B) = P(A) + P(B)\r<BR>\n" );
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document.write( "1/2 = 1/3 + 1/3\r<BR>\n" );
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document.write( "1/2 = 2/3\r<BR>\n" );
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document.write( "This is false, so the events are NOT mutually exclusive\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "The formula given above really expands to \r<BR>\n" );
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document.write( "P(A or B) = P(A) + P(B) - P(A & B)\r<BR>\n" );
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document.write( "and you can solve for P(A & B) to get\r<BR>\n" );
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document.write( "P(A & B) = P(A) + P(B) - P(A or B)\r<BR>\n" );
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document.write( "So plug in the given values to get...\r<BR>\n" );
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document.write( "P(A & B) = P(A) + P(B) - P(A or B)\r<BR>\n" );
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document.write( "P(A & B) = 1/3 + 1/3 - 1/2\r<BR>\n" );
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document.write( "P(A & B) = 2/3 - 1/2\r<BR>\n" );
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document.write( "P(A & B) = 4/6 - 3/6\r<BR>\n" );
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document.write( "P(A & B) = 1/6<BR>\n" );
document.write( " </SPAN>\n" );
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