document.write( "Question 805273: In a game, three standard dice are rolled and the number of odd values that appear is used to advance your gamepiece (for example, the roll 2-3-1 would advance your gamepiece two spaces). Produce a probability distribution for this experiment. \n" ); document.write( "
Algebra.Com's Answer #485164 by Edwin McCravy(20056)\"\" \"About 
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In a game, three standard dice are rolled and the number of odd values that appear is used to advance your gamepiece (for example, the roll 2-3-1 would advance your gamepiece two spaces). Produce a probability distribution for this experiment.
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document.write( "There are 6󬝲 = 216 ways the three dice can fall.\r\n" );
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document.write( "The number of ways to get 3 evens is 3󫢫 = 27, in which you\r\n" );
document.write( "would advance your gamepiece 0 spaces.\r\n" );
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document.write( "The number of ways to get 3 odds is also 3󫢫 = 27, in which you\r\n" );
document.write( "would advance your gamepiece 3 spaces.\r\n" );
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document.write( "That accounts for 27+27 or 54 of the 216 rolls. That leaves \r\n" );
document.write( "216-54=162 possible rolls.\r\n" );
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document.write( "The remaining 162 rolls will consist of either 2 odds and 1 even,\r\n" );
document.write( "or 2 evens and 1 odd.\r\n" );
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document.write( "There will be the same number of each, so there will be \r\n" );
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document.write( "162/2 = 81 ways to roll 2 odds and 1 even, in which you would advance \r\n" );
document.write( "your gamepiece 2 spaces\r\n" );
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document.write( "and there will be \r\n" );
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document.write( "162/2 = 81 ways to roll 2 evens and 1 odd, in which you would advance \r\n" );
document.write( "your gamepiece 1 spaces\r\n" );
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document.write( "So, \r\n" );
document.write( "the probability of moving your gamepiece 0 spaces is 27/216 = 1/8 = 0.125\r\n" );
document.write( "the probability of moving your gamepiece 1 spaces is 81/216 = 3/8 = 0.375\r\n" );
document.write( "the probability of moving your gamepiece 2 spaces is 81/216 = 3/8 = 0.375\r\n" );
document.write( "the probability of moving your gamepiece 3 spaces is 81/216 = 1/8 = 0.125 \r\n" );
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document.write( "  X           P(X)       Expect-\r\n" );
document.write( "[No. of      [Prob-      ation\r\n" );
document.write( "spaces        abil-        =\r\n" );
document.write( "moved]        ity]       X稰(X)\r\n" );
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document.write( "  0          0.125          0\r\n" );
document.write( "  1          0.375        0.375    \r\n" );
document.write( "  2          0.375        0.75\r\n" );
document.write( "  3          0.375        1.125\r\n" );
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document.write( "             1.000        2.25\r\n" );
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document.write( "You weren't asked to make the third column.\r\n" );
document.write( "So you can omit it.  However in other problems\r\n" );
document.write( "involving expectation, you will have to do that.\r\n" );
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document.write( "The expectation of 2.25 means that if you roll\r\n" );
document.write( "the three dice many times, you will average \r\n" );
document.write( "moving the gamepiece 2.25 spaces per roll.  [You \r\n" );
document.write( "will never move it 2.25 spaces, because you'll \r\n" );
document.write( "either move it 0,1,2, or 3 spaces.  However you\r\n" );
document.write( "will average moving it 2.25 spaces per roll.\r\n" );
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document.write( "Edwin
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