document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040480>Question 1040480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.\r<BR>\n" );
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document.write( "Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point.<BR>\n" );
document.write( "a. Let X = the points you have after one spin. Fill out the missing values in the table.<BR>\n" );
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document.write( "P(xi)\r<BR>\n" );
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document.write( "b. If you take one spin, what is your expected value?<BR>\n" );
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document.write( "c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.<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 #655374 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=655374\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. \r<BR>\n" );
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document.write( "A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.<BR>\n" );
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document.write( "Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point.<BR>\n" );
document.write( "a. Let X = the points you have after one spin. Fill out the missing values in the table.\r<BR>\n" );
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document.write( "Xi:::...... 3.......1.......0........-1 <BR>\n" );
document.write( "P(xi)...... 1/7....2/7.....2/7......2/7<BR>\n" );
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document.write( "b. If you take one spin, what is your expected value?<BR>\n" );
document.write( "E(Xi) = [3 + 2 + 2 + 2]/7 = 9/7 points = 1.29<BR>\n" );
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document.write( "c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.<BR>\n" );
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document.write( "Note:: A fair game has an expected value of zero.<BR>\n" );
document.write( "There are multiple ways to change Xi and or P(Xi) to achieve that result.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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