document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430376>Question 430376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are given the probabilities below:<BR>\n" );
document.write( "P(a) = 0.25<BR>\n" );
document.write( "P(B) = 0.30<BR>\n" );
document.write( "P(C) = 0.55<BR>\n" );
document.write( "P(A and C) = 0.05<BR>\n" );
document.write( "P(b and C) = 0<BR>\n" );
document.write( "P(B|A) = 0.48\r<BR>\n" );
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document.write( "A.) Are A and B independent events? Why or Why not?<BR>\n" );
document.write( "B.) Find P(A and B)<BR>\n" );
document.write( "C.) Find P (A or B)<BR>\n" );
document.write( "D.) Find P(A|B)<BR>\n" );
document.write( "E.) Are B and C mutually exclusive events?  Why or why not?<BR>\n" );
document.write( "F.) Are B and C independent events? Provide mathematical proof. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298921 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=298921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) A and B are not independent: P(A)*P(B)= 0.25*0.30 = 0.075.  This is not equal to P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.\r<BR>\n" );
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document.write( "B) P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.<BR>\n" );
document.write( "C) P(A or B) = P(A) + P(B) - P(A and B) = 0.25 + 0.30 - 0.12 = 0.43<BR>\n" );
document.write( "D) P(A|B) = P(A and B)/P(B) = 0.12/0.30 = 0.40<BR>\n" );
document.write( "E) B and C are mutually exclusive, because it is given that P(B and C)=0 (Definition of mutual exclusivity.)\r<BR>\n" );
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document.write( "F) P(B)*P(C) = 0.30*0.55 = 0.165<BR>\n" );
document.write( "P(B and C) = 0<BR>\n" );
document.write( "==> The two quantities are not equal, hence B and C are not independent. </SPAN>\n" );
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