document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195176>Question 1195176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You roll two six-sided fair dice.\r<BR>\n" );
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document.write( "a.  Let A be the event that either a 3 or 4 is rolled first followed by an odd number.<BR>\n" );
document.write( "    P(A) =  <BR>\n" );
document.write( " Round your answer to four decimal places.\r<BR>\n" );
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document.write( "b.  Let B be the event that the sum of the two dice is at most 7.<BR>\n" );
document.write( "    P(B) = <BR>\n" );
document.write( " Round your answer to four decimal places.\r<BR>\n" );
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document.write( "c.  Are A and B mutually exclusive events?\r<BR>\n" );
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document.write( "d.  Are A and B independent events?\r<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 #827588 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Sorry you have to put up with the idiotic responses from some tutors on this site....<br><BR>\n" );
document.write( "Your SINGLE problem contains four questions, all of which are interrelated; the post HAS TO contain all four questions.  It would be absurd to post the 4 questions in your post separately!<br><BR>\n" );
document.write( "a. P(3 or 4) on first roll = 2/6 = 1/3<BR>\n" );
document.write( "P(odd on second roll = 3/6 = 1/2<BR>\n" );
document.write( "P((3 or 4 on first) AND (odd on second)) = (1/3)(1/2) = 1/6<br><BR>\n" );
document.write( "b. P(sum at most 7) = P(2)+P(3)+P(4)+P(5)+P(6)+P(7) = (1/36)+(2/36)+(3/36)+(4/36)+(5/36)+(6/36) = 21/36 = 7/12<br><BR>\n" );
document.write( "c. The events are not mutually exclusive -- it is possible to get a 3 or 4 on the first roll and get a sum of at most 7 on the two rolls.<br><BR>\n" );
document.write( "d. The events are independent.  The probability of getting a sum of at most 7 on the two dice is not affected by the probability of getting a 3 or 4 on the first roll; and vice versa.<br><BR>\n" );
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document.write( "Dear idiot tutor @ikleyn --<br><BR>\n" );
document.write( "Your answer was NOT right; you didn't even answer the question!!!<br><BR>\n" );
document.write( "And it WAS idiotic to say that the original post shouldn't have included four different questions, because they were all part of one problem.<br><BR>\n" );
document.write( "When, oh when, will you learn not to be such an arrogant pain in the butt?<br><BR>\n" );
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