document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=994977>Question 994977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the two events A and B with P(A) = 0.4 and P(B) = 0.3. (a) If A and B are independent then compute the probability that<BR>\n" );
document.write( "(i) Both A and B happen.<BR>\n" );
document.write( "(ii) A or B happen.<BR>\n" );
document.write( "(iii) Neither A nor B happen.<BR>\n" );
document.write( "(b) Now answer parts (i)-(iii) when the events A and B are mutually exclusive instead of being independent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613873 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Probability is 0.12 that both happen.  You multiply.<BR>\n" );
document.write( "Neither happens is 0.6*0.7=0.42.  You take the complement of each and multiply <BR>\n" );
document.write( "A or B happens.  0.4+0.3-P(both)=0.7-0.12=0.58<BR>\n" );
document.write( "If they are mutually exclusive, then <BR>\n" );
document.write( "probability is 0 that both happen.  They can't by definition.<BR>\n" );
document.write( "probability A or B happens is 0.7.  There is no double counting.<BR>\n" );
document.write( "probability neither happens is 0.3.<BR>\n" );
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