document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181935>Question 1181935</A>: <I><SPAN STYLE=\"word-break: break-all;\">  In the game “Making Green”, a player spins twice. If the player gets blue in one section and yellow in the<BR>\n" );
document.write( "other, the player wins, because blue and yellow make green. The player can choose either spinner for each spin.<BR>\n" );
document.write( "Three people play the game. Player 1 spins spinner A twice. Player 2 spins spinner A once and spinner B once. Player 3<BR>\n" );
document.write( "spins spinner B twice. Who has the best chance to Make Green? \r<BR>\n" );
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document.write( "I can't add a picture, but hopefully this makes sense. Spinner A is broken down so each color (red, blue, yellow and orange) takes up 25% of the circle. Spinner B has 50% yellow and the other colors have an equal share of the other 50% (16.6% each). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811904 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=811904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "On spinner A, P(red)=P(blue)=P(yellow)+P(orange) = 1/4<br><BR>\n" );
document.write( "On spinner B, P(yellow)=1/2; P(red)=P(blue)=P(orange)=1/6<br><BR>\n" );
document.write( "Player 1 spins spinner A twice.  To get green he needs to get either blue or yellow on the first spin and the other of those two colors on the second.<BR>\n" );
document.write( "P(making green for player 1) = (2/4)(1/4) = 2/16 = 1/8<br><BR>\n" );
document.write( "Player 2 spins spinner A once and spinner B once.  To get green he needs to get either yellow on A and blue on B, or blue on A and yellow on B.<BR>\n" );
document.write( "P(making green for player 2) = (1/4)(1/6)+(1/4)(1/2) = 1/24+1/8 = 4/24 = 1/6<br><BR>\n" );
document.write( "Player 3 spins spinner B twice. To get green he needs to get either blue on the first spin and yellow on the second, or yellow on the first and blue on the second.<BR>\n" );
document.write( "P(making green for player 3) = (1/6)(1/2)+(1/2)(1/6) = 1/12+1/12 = 1/6<br><BR>\n" );
document.write( "ANSWER: Players 2 and 3 have an equal probability of making green; player 1 has a lower probability of making green.<br><BR>\n" );
document.write( "NOTE: Don't use the approximation 16.6% for the probability of getting red, blue, or orange on spinner B. Keep those probabilities as the fraction 1/6.  You want your calculations to be exact, not approximate.<br><BR>\n" );
document.write( "In this particular problem, since the probabilities turn out to be equal for players 2 and 3, using the approximate percentage 16.6% would make the probabilities for those two players slightly different, giving the wrong answer to the question.<br><BR>\n" );
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