document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998749>Question 998749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Based on the following results from a recent survey for a telecommunication company, would you say that it is equally likely for customers of this company to access customer service through each of the four different channels? In terms of customer service, what is the implication for the company from a staffing perspective?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Channel	Preferred choice for customer service<BR>\n" );
document.write( "1-800 number to the call centre	345<BR>\n" );
document.write( "Email	216<BR>\n" );
document.write( "Online Chat	84<BR>\n" );
document.write( "Visit to a store	143 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What is wrong with the following statements? Please explain. <BR>\n" );
document.write( "a.	P(A) = -0.3<BR>\n" );
document.write( "b.	P(Ac)=0.6 given that P(A) = 0.3<BR>\n" );
document.write( "c.	P(A or B) = 0.7 if P(A) =0.4 and P(B) =0.3<BR>\n" );
document.write( "d.	P(A and B) is always greater than 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Given that P(A)=0.64, P(B)=0.42 and P(A and B) = 0.3, calculate the following: <BR>\n" );
document.write( "a.	P(Bc)<BR>\n" );
document.write( "b.	P(A or B)<BR>\n" );
document.write( "c.	P(the complement of the event “A and B”)<BR>\n" );
document.write( "d.	P(A|B)<BR>\n" );
document.write( "e.	P(B|A)<BR>\n" );
document.write( "f.	Are Events A and B independent? Please use probabilities to justify your answer.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616489 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=616489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first part to get you started\r<BR>\n" );
document.write( "\n" );
document.write( "=================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What is wrong with the following statements? Please explain. <BR>\n" );
document.write( "a.	P(A) = -0.3<BR>\n" );
document.write( "b.	P(Ac)=0.6 given that P(A) = 0.3<BR>\n" );
document.write( "c.	P(A or B) = 0.7 if P(A) =0.4 and P(B) =0.3<BR>\n" );
document.write( "d.	P(A and B) is always greater than 0 \r<BR>\n" );
document.write( "\n" );
document.write( "=================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You cannot have a negative probability. The probability MUST be between 0 and 1 (inclusive).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(A^c) + P(A) = 1 is always true. But notice how 0.6 and 0.3 do not add to 1. So we have a contradiction here. If P(A^c) = 0.6, then P(A) = 0.4. Or if P(A) = 0.3, then P(A^c) = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "c)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(A or B) = P(A) + P(B) - P(A and B)<BR>\n" );
document.write( "P(A or B) = P(A) + P(B) - P(A)*P(B) ... assuming A and B are independent<BR>\n" );
document.write( "P(A or B) = 0.4 + 0.3 - 0.4*0.3<BR>\n" );
document.write( "P(A or B) = 0.7 - 0.12<BR>\n" );
document.write( "P(A or B) = 0.58\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So P(A or B) should equal 0.58. P(A or B) is only equal to 0.7 IF events A and B are mutually exclusive. I.e. when P(A and B) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "d)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The statement \"P(A and B) is always greater than 0 \" is false because it is possible for P(A and B) to be equal to zero. It is possible for events A and B to be mutually exclusive. Two events are mutually exclusive when they cannot happen at the same time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Event A: Rolling a 5 on a single die<BR>\n" );
document.write( "Event B: Rolling a 6 on a single die (same die as event A) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );