document.write( "Question 1197919: James designed a game that uses a spinner with twelve equal sectors numbered 1 to 12. If the spinner stops on an odd number, a player gains that number of points. However, if the spinner stops on an even number, the player losses that number of points.\r
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\n" ); document.write( "\n" ); document.write( "a) Show the probability distribution of points in this game (table only)\r
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\n" ); document.write( "\n" ); document.write( "b) What is the expected number of points per spin?\r
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\n" ); document.write( "\n" ); document.write( "c) Is the game fair? Explain
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Algebra.Com's Answer #831394 by math_tutor2020(3817) $\"\"$ $\"About$

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Spinning a...	Points Won	Probability
1	1	1/12
2	-2	1/12
3	3	1/12
4	-4	1/12
5	5	1/12
6	-6	1/12
7	7	1/12
8	-8	1/12
9	9	1/12
10	-10	1/12
11	11	1/12
12	-12	1/12

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\n" ); document.write( "\n" ); document.write( "X = number of points won
\n" ); document.write( "P(X) = probability of winning X points\n" ); document.write( "\n" ); document.write( "

X	P(X)
1	1/12
-2	1/12
3	1/12
-4	1/12
5	1/12
-6	1/12
7	1/12
-8	1/12
9	1/12
-10	1/12
11	1/12
-12	1/12

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\n" ); document.write( "\n" ); document.write( "Part (b)\r
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\n" ); document.write( "\n" ); document.write( "Form a third column labeled X*P(X)
\n" ); document.write( "As you can probably guess, this column represents us multiplying each X and P(X) value
\n" ); document.write( "Eg: -2*(1/12) = -2/12
\n" ); document.write( "I'll leave the fractions un-reduced\n" ); document.write( "\n" ); document.write( "

X	P(X)	X*P(X)
1	1/12	1/12
-2	1/12	-2/12
3	1/12	3/12
-4	1/12	-4/12
5	1/12	5/12
-6	1/12	-6/12
7	1/12	7/12
-8	1/12	-8/12
9	1/12	9/12
-10	1/12	-10/12
11	1/12	11/12
-12	1/12	-12/12

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\n" ); document.write( "\n" ); document.write( "Then we add up everything in the X*P(X) column.
\n" ); document.write( "We'll add the numerators\r
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\n" ); document.write( "\n" ); document.write( "1+(-2)+3+(-4)+5+(-6)+7+(-8)+9+(-10)+11+(-12) = -6 which is the numerator in the answer before reducing.\r
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\n" ); document.write( "\n" ); document.write( "Adding up all the fractions in the X*P(X) column leads to -6/12 = -1/2
\n" ); document.write( "The player expects to lose, on average, 1/2 = 0.5 points per game.\r
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\n" ); document.write( "\n" ); document.write( "Answer: -1/2 = -0.5\r
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\n" ); document.write( "\n" ); document.write( "Part (c)\r
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\n" ); document.write( "\n" ); document.write( "The game is not fair because the expected value (in part b) is not zero.
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