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Math Help - Probability - Average number to get all toys

  1. #1
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    Question Probability - Average number to get all toys

    So I've been having some massive trouble with this problem and after bashing my head and doing all else possible, I came here.

    Question: There are 6 toys included in a happy meal. Each is equally likely to be in the happy meal. Find the # of happy meals that you would need to buy to get all 6 toys ON AVERAGE.


    Ignore the bold at your peril.
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  2. #2
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    Re: Probability - Average number to get all toys

    Quote Originally Posted by Zystrophys View Post
    Question: There are 6 toys included in a happy meal. Each is equally likely to be in the happy meal. Find the # of happy meals that you would need to buy to get all 6 toys ON AVERAGE.
    This is a famous question. It is known as the coupon problem.
    Look at the Calculating the expectation section for the answer.
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  3. #3
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    Re: Probability - Average number to get all toys

    Thanks.

    I don't know what my teacher was thinking, giving a problem like this to high school students. Just a bit too hard for us to do.
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  4. #4
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    Re: Probability - Average number to get all toys

    Quote Originally Posted by Zystrophys View Post
    I don't know what my teacher was thinking, giving a problem like this to high school students. Just a bit too hard for us to do.
    It is relatively easy for you to calculate the answer:
    6\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac  {1}{5}+\frac{1}{6}\right)=14.7~.

    However, the logic behind the method is quite advanced as you saw.
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  5. #5
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    Re: Probability - Average number to get all toys

    The logic was hard, not the arithmetic. Especially if my teacher expected us to somehow recreate it in class.

    Thanks Plato.
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