document.write( "Question 1158125: Illinois conducts a lottery every day. Participants select three numbers between 0 and 9. A number cannot be selected more than once so a 3-digit number could be 307, for example, but not 337. Purchasing one ticket allows you to select on set of numbers. The winning number is announced on TV every night. Calculate the total number of possible outcomes.\r
\n" ); document.write( "\n" ); document.write( "1. New york also has a daily lottery in which participants select three numbers between 0 and 9. However, in New York a number may be selected more than once. What is the total number of possible outcomes?
\n" ); document.write( "2. If you purchased a ticket for $5 in Illinois and won, how much would you get if Illinois paid you according to your actual mathematical probability of winning?
\n" ); document.write( "3. If you won New York’s lottery and were paid “true odds,” how much would you expect to get for a $1 ticket?
\n" ); document.write( "4. Suppose you purchased 10 different tickets in New York’s lottery for a single drawing, what is the probability that one of your numbers would come up? \r
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Algebra.Com's Answer #781154 by Shin123(626) $\"\"$ $\"About$

You can put this solution on YOUR website!
There are 10 ways to pick the first number, 9 ways to pick the second number, and 8 ways to choose the final number, so there are $\"10%2A9%2A8=720\"$ possible outcomes.
\n" ); document.write( "1. There are $\"10%5E3=1000\"$ outcomes.
\n" ); document.write( "2. There is a $\"1%2F720\"$ chance of winning. The expected value is $\"%28x-5%29%2A%281%2F720%29-5%2A%28719%2F720%29\"$ , where x is how much you win if you win the lottery. This simplified to \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Solved by pluggable solver: Solve an equation

This is a solution to the equation:
Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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Graphical form: $\"%28x-5%29%2A%281%2F720%29-5%2A%28719%2F720%29\"$ simplifies to $\"x%2F720-5\"$
Text form: (x-5)*(1/720)-5*(719/720) simplifies to x/720-5
Cartoon (animation) form: $\"simplify_cartoon%28+%28x-5%29%2A%281%2F720%29-5%2A%28719%2F720%29+%29\"$
For tutors: simplify_cartoon( (x-5)*(1/720)-5*(719/720) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+%28x-5%29%2A%28highlight_red%28+1%2F720+%29%29+%29-5%2A%28719%2F720%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$ , $\"highlight_red%28+1%2F720+%29\"$
It becomes $\"%28x-5%29%2Ahighlight_green%28+1+%29%2Fhighlight_green%28+720+%29-5%2A%28719%2F720%29\"$ .
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Look at $\"%28x-5%29%2A1%2F720-highlight_red%28+5%2A%28highlight_red%28+719%2F720+%29%29+%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+719+%29\"$ , $\"highlight_red%28+1%2F720+%29\"$
It becomes $\"%28x-5%29%2A1%2F720-5%2Ahighlight_green%28+719+%29%2Fhighlight_green%28+720+%29\"$ .
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Look at $\"%28x-5%29%2Ahighlight_red%28+1+%29%2F720-5%2A719%2F720\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"%28x-5%29%2F720-5%2A719%2F720\"$ .
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Look at $\"%28x-5%29%2F720-highlight_red%28+5+%29%2A719%2Fhighlight_red%28+720+%29\"$ .
Factors 5 and 720 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes $\"%28x-5%29%2F720-highlight_green%28+1+%29%2A719%2Fhighlight_green%28+144+%29\"$ .
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Look at $\"%28x-5%29%2F720-highlight_red%28+1+%29%2Ahighlight_red%28+719+%29%2F144\"$ .
Multiplied numerator integers
It becomes $\"%28x-5%29%2F720-highlight_green%28+719+%29%2F144\"$ .
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Look at $\"highlight_red%28+%28x-5%29%2F720+%29-719%2F144\"$ .
Expanded term $\"1%2F720\"$ by using associative property on $\"%28x-5%29\"$
It becomes $\"highlight_green%28+1%2F720%2Ax+%29-highlight_green%28+1%2F720%2A5+%29-719%2F144\"$ .
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Look at $\"highlight_red%28+1+%29%2F720%2Ax-1%2F720%2A5-719%2F144\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"x%2F720-1%2F720%2A5-719%2F144\"$ .
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Look at $\"x%2F720-1%2Fhighlight_red%28+720+%29%2Ahighlight_red%28+5+%29-719%2F144\"$ .
Factors 5 and 720 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes $\"x%2F720-1%2Fhighlight_green%28+144+%29%2Ahighlight_green%28+1+%29-719%2F144\"$ .
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Look at $\"x%2F720-highlight_red%28+1+%29%2F144%2Ahighlight_red%28+1+%29-719%2F144\"$ .
Multiplied numerator integers
It becomes $\"x%2F720-highlight_green%28+1+%29%2F144-719%2F144\"$ .
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Look at $\"x%2F720-highlight_red%28+1%2F144+%29-highlight_red%28+719%2F144+%29\"$ .
Added fractions or integers together
It becomes $\"x%2F720-highlight_green%28+720%2F144+%29\"$ .
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Look at $\"x%2F720-highlight_red%28+720+%29%2Fhighlight_red%28+144+%29\"$ .
Factors 720 and 144 have greatest common factor (GCF) of 144. Reducing fraction.
It becomes $\"x%2F720-highlight_green%28+5+%29%2Fhighlight_green%28+1+%29\"$ .
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Look at $\"x%2F720-5%2Fhighlight_red%28+1+%29\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1%2F1+%29\"$
It becomes $\"x%2F720-5\"$ .
Result: $\"x%2F720-5\"$
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Universal Simplifier and Solver

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Done!
x/720-5

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If the expected value is $0, then Illinois will pay you $\"720%2A5=3600\"$ dollars.
\n" ); document.write( "3. The expected value is $\"%28x-1%29%2A%281%2F1000%29-1%2A%28999%2F1000%29\"$ . This simplifies into \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Solved by pluggable solver: Solve an equation

This is a solution to the equation:
Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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Graphical form: $\"%28x-1%29%2A%281%2F1000%29-1%2A%28999%2F1000%29\"$ simplifies to $\"x%2F1000-1\"$
Text form: (x-1)*(1/1000)-1*(999/1000) simplifies to x/1000-1
Cartoon (animation) form: $\"simplify_cartoon%28+%28x-1%29%2A%281%2F1000%29-1%2A%28999%2F1000%29+%29\"$
For tutors: simplify_cartoon( (x-1)*(1/1000)-1*(999/1000) )
If you have a website, here's a link to this solution.

\n" ); document.write( "

DETAILED EXPLANATION

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Look at $\"highlight_red%28+%28x-1%29%2A%28highlight_red%28+1%2F1000+%29%29+%29-1%2A%28999%2F1000%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$ , $\"highlight_red%28+1%2F1000+%29\"$
It becomes $\"%28x-1%29%2Ahighlight_green%28+1+%29%2Fhighlight_green%28+1000+%29-1%2A%28999%2F1000%29\"$ .
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Look at $\"%28x-1%29%2A1%2F1000-highlight_red%28+1%2A%28highlight_red%28+999%2F1000+%29%29+%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+999+%29\"$ , $\"highlight_red%28+1%2F1000+%29\"$
It becomes $\"%28x-1%29%2A1%2F1000-1%2Ahighlight_green%28+999+%29%2Fhighlight_green%28+1000+%29\"$ .
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Look at $\"%28x-1%29%2Ahighlight_red%28+1+%29%2F1000-1%2A999%2F1000\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"%28x-1%29%2F1000-1%2A999%2F1000\"$ .
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Look at $\"%28x-1%29%2F1000-highlight_red%28+1+%29%2Ahighlight_red%28+999+%29%2F1000\"$ .
Multiplied numerator integers
It becomes $\"%28x-1%29%2F1000-highlight_green%28+999+%29%2F1000\"$ .
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Look at $\"highlight_red%28+%28x-1%29%2F1000+%29-999%2F1000\"$ .
Expanded term $\"1%2F1000\"$ by using associative property on $\"%28x-1%29\"$
It becomes $\"highlight_green%28+1%2F1000%2Ax+%29-highlight_green%28+1%2F1000%2A1+%29-999%2F1000\"$ .
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Look at $\"highlight_red%28+1+%29%2F1000%2Ax-1%2F1000%2A1-999%2F1000\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"x%2F1000-1%2F1000%2A1-999%2F1000\"$ .
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Look at $\"x%2F1000-highlight_red%28+1+%29%2F1000%2Ahighlight_red%28+1+%29-999%2F1000\"$ .
Multiplied numerator integers
It becomes $\"x%2F1000-highlight_green%28+1+%29%2F1000-999%2F1000\"$ .
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Look at $\"x%2F1000-highlight_red%28+1%2F1000+%29-highlight_red%28+999%2F1000+%29\"$ .
Added fractions or integers together
It becomes $\"x%2F1000-highlight_green%28+1000%2F1000+%29\"$ .
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Look at $\"x%2F1000-highlight_red%28+1000+%29%2Fhighlight_red%28+1000+%29\"$ .
Reduce similar several occurrences of $\"highlight_red%28+1000+%29\"$ to $\"highlight_green%28+1+%29\"$
It becomes $\"x%2F1000-highlight_green%28+1+%29\"$ .
Result: $\"x%2F1000-1\"$
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Universal Simplifier and Solver

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Done!
x/1000-1

\n" ); document.write( " So you would be payed $1,000. \n" ); document.write( "

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