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Math Help - probability

  1. #1
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    probability

    Not sure how to go about this one..

    Johnís wallet contains two $20-bills, one $10-dollar bill, and three $5-dollar bills. On this particular summer day, Johnís friend Eddy is visiting and Eddyís wallet contains one $20, three $10s, and one $5. Both wallets look the same and are sitting together on the table. When little Jenny hears the ice cream truck coming she asks her dad John if she can have
    some money for an ice cream. He tells her she can go grab a bill out of his wallet. She runs to the table, randomly grabs a bill out of one of the wallets, buys an ice cream for $2 and then returns the change to one of the wallets (not remembering which one she took the money
    from). A tree diagram would be useful here!
    (a) What is the probability that Eddy goes home with more money than he came with?
    (b) What is the probability Eddy still has his $20-bill when he leaves?
    (c) If the change Jenny returns with is more than $5, what is the probability she took the money from the correct wallet?
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  2. #2
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    Hello, zackgilbey!

    I started a tree diagram, then found that we can answer
    . . the first two questions with a little "common sense."


    Johnís wallet contains two $20-bills, one $10-dollar bill, and three $5-dollar bills.
    Johnís friend Eddys wallet contains one $20, three $10s, and one $5.
    Both wallets look the same and are sitting together on the table.
    When little Jenny hears the ice cream truck coming she asks her dad John
    if she can have some money for an ice cream.
    He tells her she can go grab a bill out of his wallet.
    She runs to the table, randomly grabs a bill out of one of the wallets,
    buys an ice cream for $2, and then returns the change to one of the wallets.

    (a) What is the probability that Eddy goes home with more money than he came with?

    If Eddy has a profit, Jenny must have taken a bill from John's wallet.
    . . This happens with probabiity \tfrac{1}{2}.

    She returns with the change and puts it in Eddy's wallet.
    . . This happens with probability \tfrac{1}{2}.

    So Eddy makes a profit with probability: . \frac{1}{2}\cdot\frac{1}{2} \:=\:\frac{1}{4}




    (b) What is the probability Eddy still has his $20-bill when he leaves?

    Eddy will still have his $20-bill if one of two cases occur:

    . . [1] Jenny takes money from John's wallet: probabiity \tfrac{1}{2}

    . . [2] Jenny takes money from Eddy's wallet (probability \tfrac{1}{2}\)
    . . . . .and takes $5 or $10 (probability \tfrac{4}{5})


    Therefore: . P(\text{Eddy has his \$20 bill}) \:=\:\frac{1}{2}+\frac{1}{2}\!\cdot\!\frac{4}{5} \;=\;\frac{9}{10}



    I'm still working on a simple way to explain my answer to part (c).

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  3. #3
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    thanks... ive created a tree diagram and a and b make sense now as for part c this is what i got.

    If there is more than 5 dollars change that means it must be a $10 or $20 so I eliminated the chance of $5 bills. Jenny is still faced with choosing either John or Eddy's wallet. so 1/2 now if she chooses John's wallet correctly there is a 2/5 chance that it will be something other than a $5 (10 or 20 bill) Therefore would the answer be

    (1/2) . (2/5)
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