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Math Help - Expected Value of Collecting a set

  1. #1
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    Expected Value of Collecting a set

    Can someone explain the maths involved in being able to solve this to me please:

    Every packet of Captain Crunch Chips comes with a randomly inserted letter: C, H, I, or P. If you can collect one of each letter, you will win a free packet of chips. Each letter is equally likely, what is the expected number of chip packets you need to open to win a free packet?


    I can find the probability of getting it in four goes, and five etc with work (probably do a probability tree). And have used a quick simulation to get a result of 7.4, but am sure that there must be a systematic way to solve it. Would also like to then be able to generalize it to a problem that would have more than 4 possible picks etc.

    Thanks
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  2. #2
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    Re: Expected Value of Collecting a set

    Quote Originally Posted by Mahanen View Post
    Can someone explain the maths involved in being able to solve this to me please:
    Every packet of Captain Crunch Chips comes with a randomly inserted letter: C, H, I, or P. If you can collect one of each letter, you will win a free packet of chips. Each letter is equally likely, what is the expected number of chip packets you need to open to win a free packet?
    This is a very famous and much discussed problem.
    It is not easy to understand its solution.
    But here is the solution.
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