SOLUTION: 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

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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.
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?
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?
3. If you won New York’s lottery and were paid “true odds,” how much would you expect to get for a $1 ticket?
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?





Answer by Shin123(626) About Me  (Show Source):
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.
1. There are 10%5E3=1000 outcomes.
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
Solved by pluggable solver: Solve an equation
This is a solution to the equation:
Your Result:


YOUR ANSWER


  • 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.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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

Universal Simplifier and Solver


Done!
x/720-5

If the expected value is $0, then Illinois will pay you 720%2A5=3600 dollars.
3. The expected value is %28x-1%29%2A%281%2F1000%29-1%2A%28999%2F1000%29. This simplifies into
Solved by pluggable solver: Solve an equation
This is a solution to the equation:
Your Result:


YOUR ANSWER


  • 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.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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

Universal Simplifier and Solver


Done!
x/1000-1
So you would be payed $1,000.