document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465430>Question 465430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose A and B are events with P(A) = 1/4, P(B) = 2/5, and P(A or B) = 1/2.\r<BR>\n" );
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document.write( "a) Are the events A and B mutually exclusive? Explain your reasoning.\r<BR>\n" );
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document.write( "b) What is P(A and B)?\r<BR>\n" );
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document.write( "c) Are the events A and B independent? Explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318959 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=318959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose A and B are events with P(A) = 1/4, P(B) = 2/5, and P(A or B) = 1/2. <BR>\n" );
document.write( "a) Are the events A and B mutually exclusive? Explain your reasoning.<BR>\n" );
document.write( "no as you can see in the answer to \"b\" (below).<BR>\n" );
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document.write( "b) What is P(A and B) <BR>\n" );
document.write( "= P(A) + P(B) - P(A or B)<BR>\n" );
document.write( "= (1/4) + (2/5) - (1/2) <BR>\n" );
document.write( "= (13/20)- (10/20) = 3/20<BR>\n" );
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document.write( "c) Are the events A and B independent? <BR>\n" );
document.write( "Check: P(A)*P(B) = P(A|B) ???<BR>\n" );
document.write( "(1/4)(2/5) = P(A and B)/P(B)  ???<BR>\n" );
document.write( "2/20 = (3/20)/(2/5) ???<BR>\n" );
document.write( "1/10 = 6/100 ??? <BR>\n" );
document.write( "Answer: 1/10 does not equal 3/50<BR>\n" );
document.write( "So A and B are not independent.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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