document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028444>Question 1028444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the experiment of rolling two dice (one die is blue and the other is red) and the following events:<BR>\n" );
document.write( "     A: ‘The sum of the dice is 8’ and   B: ‘Both dice have even numbers’  and  C:   “The difference (absolute value) of the dice is 2”   and  D:  “the blue die has an even number”<BR>\n" );
document.write( "Find	(a)   p(A and B)  (HINT:  You cannot assume these are independent events.)<BR>\n" );
document.write( "   	(b)   p(A or B)<BR>\n" );
document.write( " 	(c)   Are A and B mutually exclusive events? To   Explain.<BR>\n" );
document.write( "(d)	Are A and B independent events?  Explain. (no explanations no points)<BR>\n" );
document.write( "(e)	Are C and D independent events? Explain.  (no explanations no points)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643627 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=643627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) P(A & B) = 3/36  = 1/12<BR>\n" );
document.write( "Of the five pairs that will give a sum of 8, only three are both even.\r<BR>\n" );
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document.write( "(b)  P(A or B) = P(A) + P(B) - P(A&B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F36+%2B+1%2F4+-+1%2F12+=+11%2F36 ALIGN=MIDDLE  ALT=\"5%2F36+%2B+1%2F4+-+1%2F12+=+11%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by the addition law of probability.\r<BR>\n" );
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document.write( "(c)  Are A and B mutually exclusive events? NO, because P(A & B) is NOT equal to zero.\r<BR>\n" );
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document.write( "(d)  Are A and B independent events? NO, because P(A) = 5/36, P(B) = 1/4, P(A&B) = 1/12, and so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28A+and+B%29%3C%3EP%28A%29P%28B%29 ALIGN=MIDDLE  ALT=\"P%28A+and+B%29%3C%3EP%28A%29P%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(e)  Are C and D independent events? YES.  P(C & D) = 4/36 = 1/9.<BR>\n" );
document.write( "Now P(C) = 8/36 = 2/9, while P(D) = 1/2.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9+=+P%28C+and+D%29+=+P%28C%29P%28D%29+=+%282%2F9%29%281%2F2%29++=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9+=+P%28C+and+D%29+=+P%28C%29P%28D%29+=+%282%2F9%29%281%2F2%29++=1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );