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anonymous

  • one year ago

You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $480 prize, two $75 prizes, and four $20 prizes. Find your expected gain or loss. (Round your answer to two decimal places.)

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  1. anonymous
    • one year ago
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    |dw:1436664920532:dw|

  2. anonymous
    • one year ago
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    how is my set up wrong???

  3. jim_thompson5910
    • one year ago
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    the table looks good. Is your book showing something else?

  4. anonymous
    • one year ago
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    no idea :P

  5. ybarrap
    • one year ago
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    Now just sum the final column to get your expected gain/loss.

  6. misty1212
    • one year ago
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    HI!!

  7. misty1212
    • one year ago
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    you want a simple way to do it?

  8. anonymous
    • one year ago
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    yea I am adding it up but it is not right

  9. misty1212
    • one year ago
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    buy all 100 tickets at $10 each how much did you spend?

  10. anonymous
    • one year ago
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    1000?

  11. misty1212
    • one year ago
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    yes of course how much money do you get back?

  12. misty1212
    • one year ago
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    if that is not clear, i can explain, it is a very simple calculation

  13. anonymous
    • one year ago
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    oh yea how would I calculate that?

  14. misty1212
    • one year ago
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    one $480 prize two $75 prizes 5 $20 prizes

  15. misty1212
    • one year ago
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    \[480+2\times 75+5\times 20=?\]

  16. anonymous
    • one year ago
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    oh right right it is 730

  17. misty1212
    • one year ago
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    you spent $1000 you get back $730 how much money did you lose?

  18. anonymous
    • one year ago
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    270$

  19. misty1212
    • one year ago
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    exactly averaged over the 100 tickets that is a loss of \(270\div 100=2.7\)

  20. jim_thompson5910
    • one year ago
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    There are 4 tickets where you win $20, not 5 tickets

  21. misty1212
    • one year ago
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    ahh so there are !

  22. anonymous
    • one year ago
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    $-1.90??

  23. misty1212
    • one year ago
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    that means you only get $710 back for a total loss of $290

  24. misty1212
    • one year ago
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    averaged over the 100 tickets it is a loss of \(290\div 100=2.9\) so your expected value i s\(-\$2.9\) per ticket

  25. anonymous
    • one year ago
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    $-2.90

  26. misty1212
    • one year ago
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    right

  27. anonymous
    • one year ago
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    thanks so much cool way to solve it but do you possibly know the mistake on my chart

  28. misty1212
    • one year ago
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    let me look

  29. anonymous
    • one year ago
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    ok thnx

  30. misty1212
    • one year ago
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    ok i see why

  31. misty1212
    • one year ago
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    when you win your prize of say $480 you have already spent $10 they do not refund your price of purchase, therefore your actual winnings are not $480 but rather $470

  32. misty1212
    • one year ago
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    same with all the other numbers

  33. misty1212
    • one year ago
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    i.e. when you win $75 it is a net gain of $65 and when you win $20 it is a net gain of $10

  34. misty1212
    • one year ago
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    do it using your method but with the new numbers and you will get it

  35. ybarrap
    • one year ago
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    The probability that you spend 10 dollars on the ticket if you play is 1: |dw:1436674572521:dw| $$ E[{\bf{X}}]=-10+.01(480)+.02(75)+.04(20)=-2.90 $$ Where \({\bf X}\) is your expected gain/loss.

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