document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033911>Question 1033911</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.12, the probability that a roll comes up 1 or 2 is 0.45, and the probability that a roll comes up 2 or 3 is 0.47 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)\r<BR>\n" );
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document.write( "in dollars </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648739 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=648739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is given that p(1) = 0.12.  Since p(1 or 2) = 0.45, then by mutual exclusivity, p(2) = 0.33.  Since p(2 or 3) = 0.47, then again by mutual exclusivity p(3) = 0.14.  This gives p(4) = 1 - 0.12 - 0.33 - 0.14 = 0.41.\r<BR>\n" );
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document.write( "==> Your expected winning is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%29+=+1%2A0.12+%2B+2%2A0.33+%2B+3%2A0.14+%2B+4%2A0.41+=+2.84 ALIGN=MIDDLE  ALT=\"E%28X%29+=+1%2A0.12+%2B+2%2A0.33+%2B+3%2A0.14+%2B+4%2A0.41+=+2.84\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therefore your expected winning is $2.84. </SPAN>\n" );
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