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 #318956 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318956\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)  Two events A and B are mutually exclusive if P(A) + P(B) = P(A U B).<BR>\n" );
document.write( "P(A) + P(B) = 1/4 + 2/5 = 13/20, but P(A U B) = P(A or B) = 1/2, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28A%29+%2B+P%28B%29+%3C%3E+P%28A+U+B%29 ALIGN=MIDDLE  ALT=\"P%28A%29+%2B+P%28B%29+%3C%3E+P%28A+U+B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so A and B are not mutually exclusive.\r<BR>\n" );
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document.write( "b) P(A and B) = P(A) + P(B) - P(A or B) = 3/20 = 0.15\r<BR>\n" );
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document.write( "c) Two events A and B are independent if P(A)*P(B) = P(A and B).<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10+=+P%28A%29%2AP%28B%29+%3C%3E+P%28AandB%29+=+3%2F20 ALIGN=MIDDLE  ALT=\"1%2F10+=+P%28A%29%2AP%28B%29+%3C%3E+P%28AandB%29+=+3%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so A and B are not independent. </SPAN>\n" );
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